Rather than dividing Christendom in "Catholic, Orthodox, Protestant," I'll rather divide it in "Western Protestant, Western Apostolic, Eastern Apostolic." Note that by "Apostolic" I mean here that Holy Tradition plays a major role in the faith.
But first, let me define the various Eucharistic theologies:
- Transubstantiation: The bread and wine become substantially the Body and Blood of Jesus, that is, the Eucharist.
- Consubstantiation: The Eucharist is substantially bread and wine, and also substantially the Body and Blood of Jesus.
- Spiritual presence: The Euchairst is bread and wine, but Jesus's Body and Blood are spiritually present within.
- Mystery: The Eucharist is the Body and Blood of Jesus. It's also bread and wine to the touch. I ain't gotta explain everything.
- Memoralism: The Eucharist is not the Body and Blood of Jesus, but is eaten to remind us of His sacrifice.
With that out of the way…
WESTERN PROTESTANT: Notably defined by belief in the following: We are saved by grace alone, through faith alone, in Christ alone, as proclaimed in the Scriptures alone, to the glory of God alone. Another common point of identity is the rejection of there being a real sacramental priesthood within the Church, a distinction between the bishops, as successors of the apostles, and laymen. Also note that these denominations are not strictly separated - indeed, many are one and the same in some countries, and besides, as long as they follow the notion above, they all recognize each other as being in Eucharistic communion.
- Lutheranism: A "default" position so to speak, focused on the five solae (salvation by grace alone, through faith alone, etc). Eucharistic belief is that of consubstantiation.
- Calvinism: Focused on the principles of TULIP, that is, human nature is Totally depraved, the saved are Unconditionally elected by God, Jesus's sacrifice on the cross was a Limited atonement (that is, only for the elect), the elect are saved by an Irresistible grace, and are given the Perseverance of the saints (that is, you cannot lose your salvation, only temporarily stray away from it, and if you end up not being saved, you were never actually saved to beign with). Eucharistic belief is that of spiritual presence.
- Baptists: Focused on a system of independant local Churches, there are no real sacraments (Baptism and Communion are purely symbolic, an outward expression of faith that only express what has already happened spiritually). They reject the baptism of children (and of those who cannot reasonably confess a profession of faith overall). Eucharistic belief is that of spiritual presence or of memoralism.
- Anabaptism: Like the Baptists, they reject the baptism of those who cannot reasonably confess a profession of faith, but they also believe in salvation by faith and works (rather than by faith alone), making them an outlier in Protestantism. Nowadays, the main branch of Anabaptism left are the Amish, who absolutely avoid technology and reject entirely involvement in politics or in warfare. Eucharistic belief is that of memoralism.
- Pentecostalism: Focused on the notion of spiritual gifts. There are three baptisms: baptism in water (a mere symbol of faith), baptism in the Body of Christ (which happens when one confesses their faith in Jesus), and baptism in the Holy Spirit (which happens when one has fully given oneself over to God). Baptism in the Holy Spirit confers holy gifts, the most notable of which is speaking in tongues, and it is a proof of one's salvation. Eucharistic view is that it is a mystery.
- Seventh-Day Adventism: Focused on an interpretation of the Scriptures following Ellen G. White's prophecy and exegesis. Most notably, they follow several of the commandments of the Law of Moses (like the Sabbath), and they come together on Saturdays rather than Sundays. Eucharistic belief is that of memoralism.
Other notable denominations:
- Oneness Pentecostalism (like Pentecostals but more cultish and also they're modern-day Arians)
- Messianic Judaism (Jews who become Evangelicals, or Evangelicals who roleplay as Jews, depending of who you ask)
- Quakers (all over the place)
- The Salvation Army (cool guys)
- Non-denominational (closeted Baptists usually)
cont…