Who are the "Two Parties" of the Protestants in the Treaty of Westphalia?

'The Protestants' were mainly divided into two factions within the Empire: 'Lutheran' and 'Reformed' churches, the latter often subsumed as 'Calvinists'.
This is really already spelled out within the treaty text itself, if you choose the correct one out of the two, in the same article 7, and should become more apparently clear if quoted with a bit more of surrounding context.

There is not 'one treaty of Westphalia, signed at Münster' as the source given for the question seems to suggest.
There are two, one negotiated in Münster and one in Osnabrück.

Wikipedia already naming the most prominent factions for these locations:

[…in Münster] only Roman Catholic worship was permitted, while Calvinism and Lutheranism were prohibited.

The text in question is not as the source seems to suggest from the Münster treaty (Instrumetum Pacis Monasteriensis, IPM), but from Article 7 of the Osnabrück treaty (Instrumetum Pacis Osnabrugensis, IPO). Article 7 from IPO does correspond to §47 of the IPM, but IPM lacks the the passage in question in the inquired form.

The IPO says this in Article VII:

Unanimi quoque Caesareae maiestatis omniumque ordinum Imperii consensu placuit, ut quicquid iuris aut beneficii cum omnes aliae constitutiones Imperii tum pax religionis et publica haec transactio in eaque decisio gravaminum caeteris catholicis et Augustanae confessioni addictis statibus et subditis tribuunt, id etiam iis, qui inter illos reformati vocantur, competere debeat salvis tamen semper statuum, qui protestantes nuncupantur, inter se et cum subditis suis conventis pactis, privilegiis, reversalibus et dispositionibus aliis, quibus de religione eiusque exercitio et inde dependentibus cuiusque loci statibus et subditis hucusque provisum est, salva itidem cuiusque conscientiae libertate.

Quoniam vero controversiae religionis, quae inter modo dictos protestantes vertuntur, hactenus non fuerunt compositae, sed ulteriori compositioni reservatae sunt, adeoque illi duas partes constituant, ideo de iure reformandi inter utramque ita conventum est, ut si aliquis

— Die Westfälischen Friedensverträge vom 24. Oktober 1648. Texte und Übersetzungen. (Acta Pacis Westphalicae. Supplementa electronica, 1), 2004. – Latin original text of the IPO (1648 October 24). (PDF)

In modern English this should read like:

With the unanimous consent of the Imperial Majesty and all the Imperial Estates, it has also been determined that all rights or privileges which, in addition to other Imperial laws, above all the Religious Peace and this public treaty, as well as in it the settlement of {religious} complaints (decisio gravaminum),

grant to the Estates and subjects belonging to the Catholic and Augsburg Confessions, shall also be granted to those who are called Reformed (qui inter illos reformati vocantur);

all, however, subject to treaties, privileges, reversals and other provisions (salvis … pactis, privilegiis, reversalibus et dispositionibus aliis), which the so-called Protestant estates have concluded among themselves and with their subjects, and in which everything has been determined for the estates and subjects of each place, without prejudice to the freedom of conscience of each, on account of religion and its practice, as well as what is connected therewith (salva itidem cuiusque conscienti[a]e libertate).

But because the religious disputes prevailing among the aforesaid Protestants (protestantes) have not been settled up to now, but reserved for a future agreement,

and consequently the Protestants form two parties, it has been agreed between the two {parties} on account of the Ius reformandi that if…

For comparison, an anonymous English translation of the IPO from 1710..

Contrasted to that we read in IPM §47:

[§ 47 IPM → Art. V, VII IPO] XLIX. And since for the greater Tranquillity of the Empire, in its general Assemblys of Peace, a certain Agreement has been made between the Emperor, Princes and States of the Empire, which has been inserted in the Instrument and Treaty of Peace, concluded with the Plenipotentiarys of the Queen and Crown of Swedeland, touching the Differences about Ecclesiastical Lands, and the Liberty of the Exercise of Religion; it has been found expedient to confirm and ratify it by this present Treaty in the same manner as the abovesaid Agreement has been made with the said Crown of Swedeland; also with those call'd the Reformed, in the same manner, as if the words of the abovesaid Instrument were reported here verbatim.

— Die Westfälischen Friedensverträge vom 24. Oktober 1648. Texte und Übersetzungen. (Acta Pacis Westphalicae. Supplementa electronica, 1) 2004. – Anoynmous English translation of the IPM (1710). (PDF)

So we see that within the IPO text the parties concerned are named as "Catholic", "those of the Augsburg Confession", 'as well as "those called Reformed"'. The latter two forming the Protestant faction, and, as they still remain in unsolved disputes over certain details — over a modus vivendi or what this very treaty should accomplish between them — therefore form two subfactions — or "two parties", and not 'one united front against Catholicism'.

This means we get to interpret not much more than what is meant by these words: Protestant, Reformed, Augsburg Confession

Protestant
Six princes of the Holy Roman Empire and rulers of fourteen Imperial Free Cities, who issued a protest (or dissent) against the edict of the Diet of Speyer (1529), were the first individuals to be called Protestants. The edict reversed concessions made to the Lutherans with the approval of Holy Roman Emperor Charles V three years earlier. The term protestant, though initially purely political in nature, later acquired a broader sense, referring to a member of any Western church which subscribed to the main Protestant principles. A Protestant is an adherent of any of those Christian bodies that separated from the Church of Rome during the Reformation, or of any group descended from them.

During the Reformation, the term protestant was hardly used outside of German politics. People who were involved in the religious movement used the word evangelical (German: evangelisch). For further details, see the section below. Gradually, protestant became a general term, meaning any adherent of the Reformation in the German-speaking area. It was ultimately somewhat taken up by Lutherans, even though Martin Luther himself insisted on Christian or evangelical as the only acceptable names for individuals who professed Christ. French and Swiss Protestants instead preferred the word reformed (French: réformé), which became a popular, neutral, and alternative name for Calvinists.)

So, why were these two factions even at odds with one another?

Reformed believers might in this sense also be called Calvinists, following also Zwingli, Bucer, Bullinger, Knox etc. Thus, in the terminology of the question as posed: one party are the Lutherans (accepting the Augsburg Confession), and the others are the 'Reformed', meaning Zwinglians and Calvinists.
Initially they also split from the Catholic mainline just like Lutherans did, but went one step further. The split came to a first blossoming during the Marburg Colloquy between Luther and Zwingli, when both agreed that the 'Catholic stance on transubstantiation was just wrong': during the Eucharist they agreed the bread doesn't really become the flesh of Jesus. But they differed bitterly over the correct interpretation of 1 Corinthians 11, 24:

This is my body that is for you.

Zwingli maintained this had to be interpreted as mere allegory and symbolism, while Luther insisted on a more literal reading, even allegedly clawing the Latin hoc est corpus meum into the table at which they had this discussion…

But apart from these theological refinements, very practical political consequences soured the relationship. While the Reformed mainly saw Lutheran Evangelicals as fellow Protestants in league against the common Catholic enemy within the Empire, the Lutherans remained more reserved.

Especially since they had the first mover advantage of being a recognised religion after the Confessio Augustana, with equally recognised rights following from that in the political sphere with the Augsburg Settlement of 1555. Namely, cuius regio, cuius religio — any prince administering a region may dictate the religion of its populace. This went great for Lutheran defecting from the Catholic mainline. But while that angered Catholics, and was welcomed by Reformed, when later Lutherans defected to Reformed, both Catholics and Lutherans weren't keen to see that.

One example for this would be Frederick III, Elector Palatine:

[…] he followed the Reformation, and in 1546 made a public profession of his faith. He succeeded his father John II as duke of Simmern on 18 May 1557, and became elector on 12 February 1559, on the death of Otto Henry. Under his predecessor strict Lutherans like Tilemann Heshusius, Melanchthonians, and Calvinists had found a place in the Palatinate. In the summer of 1559 bitter controversies arose among them. Theses on the Lord's Supper prepared by the Heidelberg deacon Wilhelm Klebitz provoked a bitter controversy between him and Heshusius.
When efforts at mediation failed Frederick deposed both men on 16 September 1559. To get a clear understanding of the controversy Frederick spent days and nights in theological studies and was thus led more and more to the Reformed confession.

His successor as Elector Palatinate Frederick V of the Palatinate was crowned King of Bohemia in 1619 and thus one of the main reasons that the war was internationalised to the scale we all know.

Of course, 'there is only one God', and consequently, all deviating too much from a common understanding are 'evil heretics'. And here defectors to the Reformed side mostly didn't weaken the Catholic power base but defected from Protestant Lutheranism, and thus weakened the Lutheran Protestant power base.

The main problem here is then from a legal viewpoint: Lutherans had rights and protections afforded to them from the Augsburg Peace:

The document itself had critical problems. While it gave legal basis for the practice of the Lutheran confession, it did not accept any of the Reformed traditions, such as Calvinism, nor did it recognize Anabaptism.

As equally, the Augsburg Confession plays no role in Reformed Churches..

So, for religious reasons, the two factions isolated one another, and for the reason of existing written law, the Reformed in effect placed themselves outside the agreed upon organigram of the Empire.

In 1555, [Charles V] signed the Peace of Augsburg, which resolved the problems to a large extent: everyone agreed that rulers would be allowed to convert to Lutheranism and enforce it in their domains, and that Catholic princes would have the right to enforce their religion in their domains.

But this apparently simple compromise left considerable room open for argument. The Catholic Church was an independent entity based in Rome, as well as an intrinsic part of each estate. If a ruler converted to Lutheranism, did he have the right to secularize church lands or incorporate them into his own state church? Many princes had already done so by 1555, and their right to retain former church lands was acknowledged; but the right of rulers who converted after 1555 was disputed. Catholics did not acknowledge this right, but newly converted Lutherans and Calvinists exercised it nonetheless. This created a standing grievance among Catholics.

The problem was even more acute with ecclesiastical territories. It was one thing if a secular prince converted, but what if the ruler was himself a member of the church and his lands part of the church? Since bishoprics and archbishoprics were not hereditary, Catholics argued, their rulers did not own the land, but were merely officeholders on behalf of the church. They had the right to convert, but they did not have the right to convert the territory with them; instead, they were obligated to abdicate their positions after leaving the Catholic faith. Catholics argued for a formal declaration of this “ecclesiastical reservation” in the Peace of Augsburg, but Protestants would not agree. Ferdinand I added it as a supplement to the Peace, but Protestants never accepted its validity. In practice, they were able to ignore it until 1580, when the conversion of the archbishop of Cologne led Catholics to declare war on him. The archbishopric was large and wealthy, and the ruler was one of the seven electors as well. The stakes were high, and Catholics were willing to fight. The Catholic coalition quickly won the war and not only forced the resignation of the Protestant ruler, but also established the fact that they would enforce the ecclesiastical reservation, whatever Lutherans thought about its legitimacy. Naturally, this left Lutherans embittered, not only because the Catholics were imposing their views by force, but also because it effectively removed a good part of the Empire—including three of the electorates—from any hope of converting to Protestantism.

Some Catholic ecclesiastical lands had already been converted to Lutheranism prior to the Peace of Augsburg, notably the archbishopric of Magdeburg and the bishopric of Osnabrück. The Protestant rulers of these territories made Lutheranism the state religion, but they did not truly “secularize” the bishoprics in the sense of converting them into lands with a secular title, such as county or duchy. They took the title of “administrators,” continued to rule through the cathedral chapter, and demanded their customary seat in the Imperial Diet on the spiritual bench. Catholics did not recognize their legitimacy, and refused to allow them.

The “right to reform” (ius reformandi) was also questioned in other cases. An Imperial Free City could convert to Lutheranism, but was it permitted to convert the surrounding countryside that it ruled? Many Catholics argued that it was not, since the right of reformation applied only to princes, not elected town councils; the town might reform itself, but not its external “subjects.” Similar doubts were raised about Imperial Knights. The right to reform also suffered from an even larger structural problem: it was only permitted to Lutherans.

Other Protestant groups were not included in the treaty. Among the excluded religions, Calvinism was the one with the most to lose: it was growing faster than Lutheranism by 1550, and continued to expand in the second half of the sixteenth century. In spite of the prohibition against Calvinist reformation, Elector Palatine converted his territory in 1559, the landgrave of Hesse-Kassel converted his in 1605, and the elector of Brandenburg followed suit in 1613. Lutherans objected to these conversions even more than Catholics, since all of the converted estates had previously been Lutheran. However, nothing was done about it, so these estates existed in a state of de facto outlawry.

— Derek Croxton: "Westphalia. The Last Christian Peace", Palgrave Macmillan: New York, 2013.

One central example of this political spilt within Protestants can be seen in the policy of Elector of Saxony, Johann Georg I. As a Protestant his main lines of policy were characterised as stead fast principles:

• traditional loyalty to the emperor ("Politice seint wir bäpstisch")
• pronounced distance to Protestant extremist demands
• a fundamental opposition towards foreign powers meddling in imperial affairs, even if in favour of the Protestant cause
• a radical disdain for anyone Reformed
• continued support of the content of the Peace of Prague_(1635)

This meant that Johann Georg was diametrically opposed to Friedrich V, not only in religious matters – on which calling both simply 'Protestant' seems like a misnomer — but also in political actions. For the peace negotiations this had profound repsercussions:

Another point illustrates Electoral Saxony's contradictory and at times even curious role during the Westphalian peace negotiations. Although Johann Georg I repeatedly urged the need for compromise and a quick conclusion of peace, at the same time there were very central red lines for the Dresden court on which it was not willing to compromise — or only under protest, for example the inclusion of the Reformed in the religious peace.

When, in the spring of 1648, agreement was finally reached on Art.VII of the IPO, which granted the Reformed the same rights as Catholics and Lutherans, the Dresden court was outraged and Leuber was instructed to obtain an amendment and, if necessary, to lodge his official protest, which he did on June 14–24, 1648. In view of the anti-reformist attitude of Electoral Saxony, this action is consistent, but it does not testify to an ability to act pragmatically for the sake of peace and the unity in the empire that was so often propagated.

Similarly paradoxical must have been Leuber's behavior both at the authentication of the IPO by handshake on July 27/August 6, 1648, and finally at the final signing of the treaty on October 14/24, 1648. At the former, he had to refuse his handshake. He had not been sufficiently instructed as to whether Johann Georg I was after all prepared to accept the satisfaction payments to Sweden, which he had so vehemently rejected against all odds. In October, Leuber was again faced with the problem that the Elector refused to allow the imperial estates to sign the treaty, as this contradicted his understanding of the emperor and the empire as a unity. In both cases, Johann Georg I ultimately had to bow to the majority; in both cases, his envoy, who had always advocated a willingness to compromise and a quick conclusion of peace on his behalf, appeared in the role of apparent peace resister.

— Lena Oetzel: "Prinzipientreue und selbstgewählte Isolation. Kursachsen auf dem Westfälischen Friedenskongress", in: Volker Arnke & Siegrid Westphal (eds): "Der schwierige Weg zum Westfälischen Frieden. Wendepunkte, Friedensversuche und die Rolle der 'Dritten Partei'", deGruyter, Berlin, Boston, 2021.

That represents the conventional reading of the two treaties. A more recent reading gives rise to a somewhat modern, distant yet even more salient interpretation of these two texts:
— David Myes: "Triplets: The Holy Roman Empire’s Birthing of Catholics, Lutherans, and Reformed in 1648", in: Marjorie Elizabeth Plummer & Joel F. Harrington (eds): "Names and Naming in Early Modern Germany", Berghahn Books: Oxford, New York, 2019. (p62–85, gBooks)

The two key articles (Avalon transcription) are these [my emphasis]:

XXVIII.
That those of the Confession of Augsburg, and particularly the Inhabitants of Oppenheim, shall be put in possession again of their Churches, and Ecclesiastical Estates, as they were in the Year 1624. as also that all others of the said Confession of Augsburg, who shall demand it, shall have the free Exercise of their Religion, as well in publick Churches at the appointed Hours, as in private in their own Houses, or in others chosen for this purpose by their Ministers, or by those of their Neighbours, preaching the Word of God.

and

XLIX
And since for the greater Tranquillity of the Empire, in its general Assemblys of Peace, a certain Agreement has been made between the Emperor, Princes and States .of the Empire, which has been inserted in the Instrument and Treaty of Peace, concluded with the Plenipotentiarys of the Queen and Crown of Swedeland, touching the Differences about Ecclesiastical Lands, and the Liberty of the Exercise of Religion; it has been found expedient to confirm,and ratify it by this present Treaty, in the same manner as the abovesaid Agreement has been made with the said Crown of Swedeland; also with those call'd the Reformed, in the same manner, as if the words of the abovesaid Instrument were reported here verbatim.

The Confession of Augsburg refers to those now generally termed Lutherans and recognized by the Treaty of Augsburg, which is confirmed and reaffirmed by the Treaty of Westphalia.

Likewise "those call'd the Reformed" refers to the various sects terming themselves "Reformed Churches" and generally now referred to, in the aggregate, as Calvinist.