The Roman Catholic Church teaches the doctrine of transubstantiation: the bread and wine literally become the blood and body of Christ during the giving of the sacrament. (n.b. I know some devout Catholics who don't believe this. They aren't exactly devout then, are they?)

Luther (and I presume Lutherans) however held a subtly different belief called consubstantiation. He believed that although the Real Presence of Christ is present in the bread and wine, it is only there in essence. I believe Luther likened it to the heat within an iron bar.

I knew studying the Reformation would be useful sometime :)