What is the Lutheran doctrine of consubstantiation and how does it differ from transubstantiation and a more general protestant sacramental view?

The Lutheran understanding of the Real Presence is that at the consecration, which happens through the power of the Holy Spirit, the bread and wine become the true body and blood of Christ "in, with, and under" the form and substance of bread. "In, with, and under" is the description of the Real Presence in Luther's Smaller Chatechism. I was taught that this is the understanding which best incorporates both the Communion narrative ("This is my body") and John 6:48 ("I am the bread of life") and John 6:51 ("I am the living bread come down from heaven").

The real distinction here is that for one who subscribes to the Tridentine Roman Catholic understanding, after the consecration, what looks, tastes, feels, and smells like bread isn't what it looks, tastes, feels, or smells like, but instead is something else entirely, the Body of Christ. There is no bread there because the bread has been replaced by Jesus so that it is Jesus, but looks like bread. But this contradicts Jesus' own teaching in John 6:48, 51, because if Jesus is the living bread, and there is no bread there, Jesus cannot be there either.

Lutherans do not generally use the term consubstantiation. Nor do they use the term impanation. Impanation, by analogy to the Incarnation, would imply some kind of hypostatic union between the bread and Christ (just as between the human and divine natures in Christ), which is explicitly rejected by the Solid Declaration of the Formula of Concord (6.38). The authentic Lutheran term for their own belief is sacramental union, even if consubstantiation, by analogy to the Catholic doctrine of transubstantiation, might be a helpful descriptor. However, in discussing any theological tradition, it is best to stick to the terminology authentic to that tradition, which again is not consubstantiation, but sacramental union.

That said, the differences between the Lutheran view and the Catholic view can be gathered from the relevant rejected propositions in the Formula of Concord (6.108-110).

1. The papistic transubstantiation, when it is taught that the consecrated or blessed bread and wine in the Holy Supper lose entirely their substance and essence, and are changed into the substance of the body and blood of Christ in such a way that only the mere form of bread and wine is left, or accidentia sine subiecto (the accidents without the object); under which form of the bread, which nevertheless is bread no longer, but according to their assertion has lost its natural essence, the body of Christ is present even apart from the administration of the Holy Supper, when the bread is enclosed in the pyx or is carried about for display and adoration. For nothing can be a sacrament without God's command and the appointed use for which it is instituted in God's Word, as was shown above.

2. We likewise reject and condemn all other papistic abuses of this Sacrament, as the abomination of the sacrifice of the mass for the living and dead.

3. Also, that contrary to the public command and institution of Christ only one form of the Sacrament is administered to the laity; as these papistic abuses have been thoroughly refuted by means of God's Word and the testimonies of the ancient Church, in the common Confession and the Apology of our churches, the Smalcald Articles, and other writings of our theologians.

Going from bottom to top, we can pick out

• The Lutherans taught that it was necessary to distribute both species in the administration of the sacament (i.e. both the bread and the wine, whereas the common practice in the Catholic west for various reasons was to distribute only the bread to the laity).
  • They rejected the Catholic belief that the mass was a true sacrifice that benefited to the living and the dead (remember that the Lutherans also rejected purgatory and indulgences).
  • They rejected the Catholic practices such as the reservation of the Sacrament (whether for the sick or for later masses) and processions (see especially the Feast of Corpus Christi), saying that Christ in such cases is not present (their dictum being, nihil habet rationem sacramenti extra usum a Christo institutum), and implying, as you noted, that these practices are idolatrous.
  • Finally, probably most significant, while affirming that Christ is truly and substantially present (which is what was written earlier in the Augsburg Confession (see Article X)), they taught that the bread remained true bread (in substance and not merely in accident) and was sacramentally united to the substance of Christ's body, whereas the Catholic teaching repeated at the Council of Trent is that the substance bread (and wine) is converted into the substance of Christ's body and blood. From the Formula of Concord (6.35,37):

For the reason why, in addition to the expressions of Christ and St. Paul (the bread in the Supper is the body of Christ or the communion of the body of Christ), also the forms: under the bread, with the bread, in the bread [the body of Christ is present and offered], are employed, is that by means of them the papistical transubstantiation may be rejected and the sacramental union of the unchanged essence of the bread and of the body of Christ indicated... Even as many eminent ancient teachers, Justin, Cyprian, Augustine, Leo, Gelasius, Chrysostom and others, use this simile concerning the words of Christ's testament: This is My body, that just as in Christ two distinct, unchanged natures are inseparably united, so in the Holy Supper the two substances, the natural bread and the true natural body of Christ, are present together here upon earth in the appointed administration of the Sacrament.

That is a basic (though not comprehensive) overview of differences. So why are they important? If nothing else it is important to understand a party according what they actually profess to believe and not merely from hearsay. Besides that, the differences in eucharistic beliefs are in many ways symptomatic of larger differences. Notably, Luther rejected the Catholic Church's view of her magisterium as an infallible teaching authority (manifested in decrees of ecumenical councils or the ex cathedra decrees of the pope). The rejection of the idea of the sacrifice of the mass is also symptomatic of the Lutheran understanding of sola fide. And this discussion is also ignoring many other relevant differences, such as the understanding of the priesthood. However, while the Lutherans did depart far from the beliefs of their mother religion, it might be eye-opening to see that (despite the inclinations of certain individuals) never departed from the belief that Christ was truly, substantially present in the sacrament, and in fact, were more opposed to these other Protestants (whom they called Sacramentarians) than the Catholics they had broken away from.

For more detailed reading, consult the Lutheran confessional documents: - The Solid Declaration of the Formula of Concord - The Augsburg Confession - The Small Catechism - The Large Catechism - The Smalcald Articles

Consubstantiation is not Lutheran theology. Lutheran theology rejects consubstantiation in favor of "Sacramental Union" [sacramentatem unionem]. See the Book of Concord, "The Solid Declaration of the Formula of Concord"; Sect. VII "The Holy Supper"; esp. subpara. 38.

Lutheran theology holds that the True Body and True Blood of Christ are present in the Sacrament of the Altar both mystically and physically. "The Solid Declaration of the Formula of Concord [Sect. VII "The Holy Supper"] connects this Mystery with the Incarnation ("... the Word became flesh ... ."). No attempt is made to explain that which "surpasses all understanding." Instead, the doctrine is simply asserted, backed with references to, of course, the Scriptures, and also to "Justin, Cyprian, Augustine, Leo, Gelasius, Chrysostom and others" [ibid, subpara. 37]. The True Body and True Blood of Christ are held to be present physically: "... the Lord's bread in the Supper is His true natural body, which the godless or Judas received with the mouth, as well as did St. Peter and all the saints ... " [ibid. subpara. 33]. Thus we see that the Real Presence of the True Body and True Blood of Christ are held to be present mystically and physically as an objective reality, quite apart from the faith or ideas or notions of those who receive them "orally" and quite apart from the "wickedness" or unworthiness of the priest* who celebrates the Mass* and administers the elements [ibid. subpara. 32]. However, Lutheran teaching also holds that the Sacrament does not "bring justification just by taking part" in it, but rather that "a faith which believes in the forgiveness of sins is needed ..." [See the unaltered Augsburg Confession, Art. XIII, para. 3.].

• (the terms used in the Lutheran confessions)

It is also--how shall I put it?--less than precise to say that Luther and the Lutheran reformers held such things as Corpus Christi processions to be "idolatrous." It is true that Luther used the words "vain idolatry" to refer specifically to Corpus Christi processions, but this was in one of his "Table Talks," not in any "official" writings or in any of the Confessions. Luther died in 1546, but Lutheran calendars retained Corpus Christi until 1600 [See Frank Senn: Christian Liturgy: Catholic and Evangelical, Fortress Press, 1997. p. 344. ISBN 0-8006-2726-1]. Luther's objection was that Christ had instituted the Sacrament of the Altar for specific purposes, and that that purpose was not for processions but for the forgiveness of sins; for awakening and strengthening faith in those who receive it; and for comforting the faithful. The Augsburg Confession [Art. XV "Of Church Customs"] says quite clearly that "Church customs [...] such as holy days, festivals, and the like [...] may be practiced only if they can be used without sinning. [...] But people must be strongly reminded that such customs [are not done] in order to earn salvation" [Augsburg Confession, Art. XV]. This of course, is connected with the Lutheran emphasis on salvation "by grace through faith" and not through works, "lest any man should boast" [Ephesians 2: 8-9].

And this was written by George III, Prince of Anhalt-Dessau and Prince of Anhalt-Plötzkau [1507-1553], priest, and one of the driving forces in the Lutheran Reformation: "Now, here we are not saying that one should not worship our dear Lord Jesus Christ in this Sacrament, being present, or that one should not hold this Sacrament with all honor and reverence. On the contrary, since these divine, almighty, true words are believed, all of this follows of itself, and not only in external gestures but also both externally and, first and foremost, in the heart, spirit, and truth. On account of this, such adoration of Christ is not thereby cancelled, but much rather, confirmed. For where the Word is rightly seen, considered and believed, the adoration of the Sacrament will happen of itself. For whoever believes that Christ's body and blood are there (as there is plenty of evidence so to believe, and it is necessary so to believe), he cannot, to be sure, deny his reverence to the body and blood of Christ without sin. For I must confess that Christ is there when His body and blood are there. His words do not lie to me, and He is not separate from His body and blood."

As to whether Lutheran churches do or do not reserve the consecrated bread as the True Body of Christ, I myself have seen tabernacles containing the Reserved Host in Finland and in Latvia. In Finland, at the cathedrals in Turku and Helsinki; in Latvia at the Cathedral in Riga.