Transubstantiation is a more recent concept. The Latin Church put more effort into trying to logic out how the various miracles (Christ's presence in the Eucharist is considered a miracle) work than either the Orthodox or Eastern Catholic churches and this is the most famous result of that. It comes from Thomas Aquinas and his successors applying Aristotelian metaphysics to Christian theology. Summa Theologica is Aquinas's definitive work.

Real presence is a much older concept and not all who affirm real presence affirm transubstantiation (which is mostly limited to Catholics and high-church Anglicans).

Various writings of early church leaders endorse real presence. The most easily accessible is Paul's first letter to the Corinthians in the New Testament. Other church leaders, such as Clement of Rome and Ignatius of Antioch affirm it too. One of the most important Early Church theologians was Irenaeus, who affirmed it in his writings, such as Against Heresies.