The Christian Church naturally was started in the Middle East. As it spread across the then known world, each nation and nationality added to the traditions and rituals of the Christian services. Two heritages dominate Christian worship today: the Eastern and the Western. Western Christianity had as its focus the societies of western and northern Europe, most notably Rome. Eastern Christianity has as its early focus the "eastern capitol of the Roman Empire," that is Constantinople (or as it had been called Byzantium).
For the first few centuries of Christian worship there were five great apostolic churches. These churches were located in the most important, or powerful, or religiously significant cities of the ancient world: Rome, Constantinople, Antioch, Jerusalem, and Alexandria. It is from the Roman church that most European and American churches draw their traditions and rituals. The four eastern churches drew their inspiration from the stylings and teachings of Constantinople. The Eastern Christians are most often called "Greek" because of the Greek empires in the eastern Mediterranean, but a more accurate term would be Byzantine Christians since their style of worship was patterned after the church at Byzantium.
Because of the many twists of history, the Eastern Christian churches today belong to many groups and categories (Greek Orthodox, Melkite, Coptic, Antiocian, Ethiopian Coptic, Russian Orthodox, Ruthenian, Ukrainian, a host of others). Some of these churches are self-governing, some of these churches are members of larger bodies, some consider themselves to be a part of the Catholic Church and others consider themselves to be of the Orthodox faith.
Eastern Catholic Churches are groups of Christians whose traditions are based on the style of Constantinople but are in union with the church of Rome. The Eastern Catholic is a member of the Catholic Church, under the authority of the Vatican and the Pope, but worshipping within a different organizational structure.