Full disclosure I am neither Catholic nor Lutheran, and the church i attended practices either Memorialism or Receptionism.
|Transubstantiation|Upon consecration by the priest the Bread and Wine completely changes into the actual body of Christ, and Christ’s presence is in the Bread and Wine (Real Presence). |Roman Catholics|
|:-|:-|:-|
|Consubstantiation|A sacramental union between the Bread and Wine with Christ. Christ’s body and blood is now present in the form of the bread and wine. ELI5: The bread and wine is still bread and wine, but Christ is also present in/with/under the bread and wine. I have seen multiple analogies, but the one that seem to make the most sense to me is one of sponge and water (it’s a bit weak because it implies you can remove the water from the sponge, while in Consubstantiation, it has been joined as one) |Lutherans|
|Divine Lithurgy|Accepts that Christ is present in the elements of the Eucharist but does not attempt to explain how, calling it a divine mystery|Orthodox|
|Memorialism|The bread and wine symbolizes the body and blood of Christ but Christ is not physically (and/or spiritually) present in the elements|most other groups|
|Receptionism|Christ is not physically present in the elements but is spiritually present in the elements|Reformed + Presbyterian|
Here’s a [really long document](http://faculty.cord.edu/steinwan/nv13_decock.htm), with a lot of terrible formatting, if you want to read it. And if you read it, you will find that it says that there are many points of agreement between Catholic and Lutheran theology. And it says the matter boils down to this as the core point of disagreement:
Catholics believe that the Eucharist is a sacrament, a good work, *that we do* for God and for ourselves and for our relationship with God. It is considered a sacrificial act that earns us forgiveness from God; this is in accordance with their general belief in salvation through good works.
Lutherans believe that the Eucharistic mystery is *something that God does*, for us, and for our relationship with him. This is what makes it a mystery; we do not know how God can perform miracles. This is in accordance with our belief, like [the song we sing](https://www.youtube.com/watch?v=z6ULNZM0-0A): “For by grace, you have been saved, and even faith is not your own; it’s the gift of God for you, and not the works that you have done.”
This is a very old and fundamental difference between Catholic and Lutheran theology; arguably it is the single point of contention that sparked the entire rest of the Reformation.
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As for Eucharistic Adoration, I assume you’re referring to the thing where some churches keep a little bit of the Eucharist, and put it on public display after the sacrament.
The general context here is that five hundred and six years ago, *we were thrown out* of the Catholic Church. Moreover, we were thrown out as a minority within Christendom, and our homelands soon became the main battlegrounds for the European Wars of Religion.
It was very important to us that we could practice our faith *simply*. [For the first thousand years](https://en.wikipedia.org/wiki/Eucharistic_adoration#Catholics), nobody in the West did Eucharistic Adoration. So we stopped, and we have never resumed.
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