You didn't ask this question, but it's lurking in the one you did ask, so I'm gonna toss this in ...
Transubstantiation is the Roman attempt to explain the Real Presence, to account for it. All who believe in transubstantiation believe in the Real Presence. However, there are many, many Christians (Anglicans, Lutherans, the Orthodox, just to name a few) who believe in the Real Presence, but do not believe in transubstantiation.
I'm in the latter group. As a more-or-less conventional evangelical Protestant, I was taken more and more by the obvous testimony of the Bible that God was simultaneously everywhere (the usual doctrine of omnipresence), and also present at some locale in a way, to a degree, that He was not present on any place else.
Theophanies, for example, do not contradict God's omnipresence. God was still omnipresent when Isaiah was confronted by God in the Temple (Isaiah 6), or when God appeared to Israel at Sinai, or to Moses in the Burning Bush. Notwithstanding, He was present in a special, peculiar way in the Burning Bush, and NOT in Moses' sleeping tent some miles away. He was present within the Holy of Holies in a way that was different than omnipresence.
And, so, the Church has believed that Christ is present in the elements of the communion in a way that He is not present in your front yard. The thing that convinced me was 1 Corinthians 11. Mere bread and wine do not make people sick, or kill them. It was because they did not discern the presence of the Lord in the Eucharist that they were judged.
How God is present in one place that is different from all other places is a thorny question to ponder. Catholics (at least since Aquinas) have used transubstantiation to explain how this happens. Leaving aside whether their explanation is credible, one does not need that particular doctrine to acknowledge that the Eucharist is one way -- a quite tangible way -- that Jesus' words to His disciples are true: "I will be with you always, even until the end of the world."
The real presence bump.