Because of the Great Schism - - East-West Schism - there was a split of the Christianity into an Eastern Orthodox Catholicism and a Roman Catholicism.
This happened especially because Pope Leo III crowned Charlemagne as a Holy Roman Emperor, the Byzantine Empire did not like this and eventually, this led to a formal split that occurred in 1054.
Because of this split, the Roman Catholic Church that existed in the Byzantine Empire became Greek Orthodox Church and the Roman Catholic Church was maintained.
The Eastern Orthodox Church was no central doctrinal or governance, unlike the Roman Catholic Church, that has the Catholic pope. The Ecumenical Patriarch of Constantinople is considered as a primus inter pares of the bishops that run each church.