When people drink the Precious Blood of Jesus they drink the full Jesus. A drop of that blood is Jesus.
A drop of my blood wouldn't be me. Also, I have a special blood type and Jesus don't.
We say that we are neither our emotions nor our blood. With Jesus it is different!
What is the official teaching on this? People doesn't even like to talk or write about this!
ANSWER: The Catholic Church teaches the doctrine of "transubstantiation". If you look at any "thing" -- a person, a pet, a rock, you can think of the thing as being made up of substance (what makes it what it is) and accident (what it has, but which could be changed without affecting the substance.) If I lose my eyes, I am still me. So through a special miracle, the substance of the bread and wine become the substance of Jesus Christ, God and Man, while leaving the "accidents" (taste, texture, etc) the same. That explanation is "official" but not always easy for us to understand today.
An explanation I like better is that my body is the "sacrament" of my person. It is not the same as my person, but it is the way my person interacts with the world, thinks, feels, etc. But I believe that when my body is gone, my person will live on.
Jesus chooses to make the bread and the wine the "sacrament" of his person.
Jesus is God and Man, which makes him different from you and I.
The Catholic Church also teaches that Jesus is completely and totally present in the bread and in the wine, and to receive either is to receive Jesus.
Hope this helps.
---------- FOLLOW-UP ----------
QUESTION: And is there a difference between the presence of Jesus when He was incarnated and when He is present on the Altar? And how does what happened at the Annunciation differ from what happens at the Consecration at Mass?
You also mentioned that we have bodies. Is it only at the ressurection of our bodies that we will have a real body/soul unity?
ANSWER: There is a difference: When Jesus walked the earth, he was present to those around him just as any human being is present. On the altar he is sacramentally present. In both cases, he is really, physically present, "body and blood, soul and divinity". In the Annunciation and in the consecration, the HOly Spirit makes Jesus present. With Mary, He conceived Christ in her; with the consecration, he transforms bread and wine into Jesus.
Finally, you touch upon an important point. When we talk about "souls" and "bodies" we get the idea that they can be separated, and that "I" have a soul, and "I" have a body -- suggesting that there is "I", my soul, and my body. John Paul II tried to look at this differently -- I am a person. My body is the sacrament of my person. My body is the way my person communicates, expresses itself, etc. It is essential that my person has a body, thus the idea of resurrection. What happens between death and resurrection is unclear (to God there is no time) -- but in some way God preserves my person until the resurrection. Hope this helps.
---------- FOLLOW-UP ----------
I hope I don't missunderstand you here: if the centurion/soldier had at the Cross bee drinking the Blood of Jesus it would be the same as doing so at a Mass?
It would be the same insofar as both are the blood of Jesus. However, in the blood (transubstantiated wine) is the sacramental presence, whereas in the blood at the cross, that is physical presence. The sacramental presence is simply, a miracle. The physical presence (only) is not. In the sacramental presence there is physical presence.
If I have a picture of my grandmother, I could say that in a way, the picture makes her present to me. That of course is more a figure of speech than a reality, but nevertheless, there is a difference between the picture of my grandmother and a picture of a horse to me. Because Jesus is God, he makes himself present in the bread and wine (and the bread and wine no longer exist) through a miracle, with every Mass. And he makes himself totally present in every particle of the host and every drop of the wine. So there is a difference.