Christendom is divided broadly into two main groups: Eastern Orthodox and Western Catholic (âorthodoxiaâ is a Greek word meaning âright praise,â âkatholikosâ is Greek for universal; both groups consider themselves both orthodox and universal, of course). The theological and practical differences are probably not worth going into, but suffice it to say that they are basically associated with the Eastern and Western divisions of the Roman Empire, i.e., with Constantinople/Byzantium/Istanbul and with Rome, respectively. They came into conflict and separated from each other in the eleventh century.
The Eastern Orthodox are a combination of independent national churches, each with their own patriarchs. The Bishop of Rome, also known as the Pope, has always been considered the Patriarch of the entire West. The various Protestant denominations that have arisen since the time of Martin Luther are basically different forms of Western Christianity, and what is now called Roman Catholicism is the portion of the Western Church that remained loyal to the Pope. These various Western denominations vary wildly in their degree of adherence to what is commonly called the Apostolic tradition (the Roman Catholics, of course, retain it fully); whereas the Orthodox churches remain, as I understand it, fairly close in terms of theology, polity, and discipline.
Nowadays, Eastern and Western Christianity, in all their forms, are found around the world, so the designations are used more in the nature of convenient tags than as descriptive terms.