Hypostasis: not 100% identical with “person,” but that’s generally the accepted definition. Jesus only has one of those. Not synonymous with corporeal body (per the Father and Spirit).
Nature: The “what-ness” of a thing. Jesus has two of them, divine and human. A human nature is not completely synonymous with a human body, but the latter is certainly included in the former.
Enhypostasis: personal natures exist in persons. There is no such thing as a free-floating human nature. In other words, have you ever looked up in the sky and seen a “nature” just floating around? Therefore, Jesus’s divine and human natures are always in his person (or his person is of two natures). Every tradition–Roman, Orthodox, and Protestant–agrees with this.
Nestorianism: textbooks define it as “two persons” of Jesus. That’s a bit crass and the better Nestorians never said that. The more subtle point is that the one hypostasis of Jesus is formed from two previous hypostases. That said, I’ve never actually met someone who holds that view. In any case, if Jesus’s human nature is going to be in two places at the same time, and if what we said about enhypostasis is true, then Jesus’s person must be in two places at one time. Thus, two persons of Jesus. That is Nestorianism. It is a heresy.
Sessional Reign of Christ: Jesus bodily ascended to the right hand of the Father. He is ruling there. He will stay there until the Parousia. If Jesus only has one hypostasis, and we rule out Nestorianism, then he cannot be bodily in a million Eucharists. Acts 3 says “Heaven must receive him until the times of restoration.” That means Jesus’s person must stay in heaven. (I do not deal with the issue of people who say they saw visions of Jesus. Perhaps they did. I dispute whether Jesus personally, bodily appeared to them).
Spirit as Vicar: If Jesus is in heaven, then who is his vicar on earth? Jesus said the Spirit.