Rulers' titles in Middle Age Italy

For centuries in the Middle Ages, in many regions of Europe there were not kings, but dukes, archdukes, etc. For instance, in Italy one had the Archduke of Tuscany and the Duke of Piedmont (until 1720) or the Duke (Doge) of Venice, etc. They were completely autonomous entities, but they were not kings. Apparently in some cases, this mattered a lot: the Duke of Piedmont gave up Sicily in 1720 in order to get Sardinia, with which he could finally be considered King of Sardinia (which included Piedmont, Liguria, Savoy etc

The OP made several errors and false assumptions. During the Middle Ages there were very few "king free" regions in Catholic Europe. Pagan rulers might not have been counted as kings by Christians, however much they might seem objectively to be pagan kings. But most areas ruled by Catholic Christians were considered part of Catholic kingdoms.

Poland was ruled part of the time by kings and part of the time by dukes with seniority over the other dukes. Lithuania was briefly a kingdom but mostly a grand duchy. Bohemia was a duchy for a few centuries before becoming a kingdom.

When King Otto the Great of Germany and Italy became emperor in 962, a large area in what is now eastern Germany and western Poland Was ruled by pagan groups tributary to the Kingdom of Germany. Later the region was converted to Christianity and organized into fiefs that were part of the Holy Roman Empire, but I don't know if those lands were supposed to be part of the Kingdom of Germany.

Thus someone who wanted to be king had a low probability that he was not already the vassal of a king who would not be pleased by him making himself king and committing treason.

A ruler using a title like baron, count, viscount, margrave, landgrave, count palatine, duke, etc. was using a title from the feudal hierarchy and thus claiming to be subordinate to a king. If he started calling himself a king he would be saying "Look everyone, I just committed treason!"

And for most of the middle ages in most areas a new king had to be crowned and anointed with holy oil by high ranking clergy, needing their approval of how he became king.

Examples of nobles forming kingdoms out of larger kingdoms include Count Boso of Provence in 879, Rudolph of upper Burgundy in 888 (both carved out of the West Frankish Kingdom), Count Roger II of Sicily in 1130 (formed out of Muslim and Christian territories), and Count Alfonso of Portugal in the Kingdom of Leon in 1139.

Catholic nobles also formed kingdoms out of Muslim lands such as the Kingdom of Jerusalem and out of Eastern Orthodox lands such as the kingdoms of Cyprus and Thessalonica.

The Kingdom of Sardinia did not include Savoy, Piedmont, etc. until the Congress of Vienna in 1815. It included only the Island of Sardinia until then. The Duchy of Savoy was part of the Kingdom of Burgundy or Arles, and the Principality of Piedmont was part of the Kingdom of Italy or Lombardy.

Before 1720 the title of victor Amadeus was:

Vittorio Amedeo per gratia di Dio Re di Sicilia, di Gerusalemme e di Cipro, Duca di Savoia, Monferrato, Aosta, Ciablese e Genevese, Prencipe di Piemonte e d'Oneglia, Marchese d'Italia, di Saluzzo, Susa, Ivrea, Ceva, del Maro e Sesana, Conte di Mauriana, Geneva, Nizza, Tenda, Romont, Asti e Alessandria, Barone di Vaud e Faucignì, Signor di Vercelli, Pinerolo, Tarantasia, Lumellina e Val di Sesia, Prencipe del Sacro Romano Imperio, e Vicario perpetuo in Italia, ecc.

And after 1720 it was:

Nos Victorius Amedeus, Dei gratia Rex Sardiniae, Cypri ct Hyerusalem, Dux Sabaudiae, Montisferrati, Augustae Salassorum, Chablasij et Gebennensis, Princeps Pedemontis et Oneliae, Marchio in Italia, Salutiarum, Secusiae, Hiporediae, Cevae, Oristanei, Marri et Cesanae, Comes Maurianae, Genevae, Nissiae, Tendarum, Romontis, Astae, Alexandriae et Goceani, Baro Baudi et Faugigniaci, Dominus Vercellarum, Pineroli, Tarantasiae, Lumellinae et Valus Sicidae, Sacri Romani Imperil Princeps, et ejusdem in Italia Vicarius perpetuus

He still had to list all the other fiefdoms because they were outside of either the Kingdom of Sicily or the Kingdom of Sardinia and his right to rule in those fiefdoms was totally separate from his right to rule in either kingdom.

If Victor Amadeaus had tried to annex all his lands to the Kingdom of Sardinia he would have been committing treason against the kings of Italy and Burgundy, who happened to be the Emperor. Did you know that after the Austrian army chased the French army out of northern Italy in the War of the Spanish Succession Emperor Joseph I collected millions of florins in imperial war tax from the states in Northern Italy in 1708?

If Victor Amadeus had proclaimed himself King of Piedmont, he would have run the risk of becoming Victim Amadeus. In England lands and titles confiscated from traitors were often restored in whole or in part to their heirs after a generation or two. But in the Holy Roman Empire confiscated lands were usually gone and lost forever for the descendants of the traitor, usually being granted to a loyal relative of the traitor. Duke Ferdinand Charles of Mantua and Montferrat had his duchies confiscated in 1708 for supporting the French, for example.

Titles of nobility literally came with the territory. Thus if you rule a principality, you are a prince, if you rule a duchy, you are a duke, and if you rule a kingdom, you are a king.

The main place it mattered was in dealing with other European nobility. In any social situation, kings got priority over dukes, who got priority over princes.

Your Savoyard example is instructive. Savoy was actually considered a duchy, and Piedmont a principality. However, the political situation was pretty much reversed, as the leadership of the kingdom was entirely based in Piedmont for most of its history. Since Sardinia was considered a kingdom, most people at the time referred to the unit as the Kingdom of Sardinia, and the Piedmont-based ruler as the King of Sardinia.

As T.E.D. already mentioned, titles were tied to the territory, and mostly didn't change unless a feudal lord higher up in the "foodchain" granted one of its vassals a higher title (it usually came with further land and possessions as well). Also, once you fulfilled certain requirements to create a title, you could do so (great example, the British Empire, which was created after it annexed other titles on the same level as kingdoms in India).

As for Italy, there were various kingdoms throughout its history. Before Rome became a republic, Rome was ruled by several kings and after the fall of the Roman Empire the land was split among many factions, among them kingdoms. Byzantium got some of southern Italy later on, but first both Odoacer and Alarich of the Visigoths founded kingdoms in Italy. They were lastly supplanted by the Longobards, who ruled most of Italy either as dukes or kings. They were then mostly conquered by the Carolingians, namely Charlemagne, which put an end to titles of the level of "king" in Italy for a long time. It also marked the annexation to the frankish empire later HRE. (You mentioned Savoia, which initailly was part of burgundy by the way). The only exception was the papal state, which to this date still is a monarchy of "king-level", where the pope still holds the title of king of the vatican and bishop of the 'holy see' -which are technically two separate titles with two separate functions (forgive the technicality, but that's what we're talking about here anyways - also check out the video about the vatican by cgp grey, it's great at explaining these title relationships).

In the following time, most dukes, counts and marquis in Italy were de iure (by right, i.e. formally) a vassal of the HRE but many were de facto autonomous, sovereign states. Exceptions here are the muslim emirate of sicily (which was later conquered by normans and became a sovereign county), the papal state and the republic of venice, which were all independent states. Sicily however retained a de iure kingdom status, but no one claimed the title. Sardinia also, after some trouble between Pisa, the Pope and the kingdom of Aragon, gained the title of kingdom. And that's important.

Now as to Savoia: it started off as a county, became a duchy (still imperial) as you already mentioned. After the war of Spanish succession it gained Sicily, which had (see above) the formal possibility of being declared kingdom. It was swapped for Sardinia, which too had the formal title of "regno di Sardegna". The Duca di Savoia actually already had some formal titles of kingdoms, remainders of the crusades, but the Duchy of Savoia still was his main title. After gaining the kingdom of Sardinia, he officially became king "Re di Sardegna", though his primary title still was "Duca di Savoia". In the 19th century the title was merged, creating the kingdom of Piedmont-Sardinia. Note that after the restoration the only other peninsular kingdom beside the papal state and the kingdom of Piedmont-sardinia was the kingdom of Two Sicilies, which also traces back it's "titolo regio" to Sicily being a king-level possession.

Long story short: he didn't swap Sicily for a titular difference, but for practicality: it was closer thus easier to rule. Also, technically most italian States were vassals of the empire, but only de iure, because the emperor always had problems controlling italian vassals. Italians were very unruly: anyone who claimed it had so many problems with it that it either lost the territory or just said "meh, i'll let you do as you please, just as long as you formally belong to me". That goes for spaniards, french, austrians and even the HRE. I'd like to add, that being a duke of the empire, the duke of Savoy still had a voting right and a place in the imperial Diet, though he never made use of it.