“The Church”, that is, the Catholic, or universal (or “undivided”) Church, never really was any of those, though many Churchmen have always wanted it to be. Probably the best model for the Church in the first, second and third Centuries was always one of strong local congregations loosely united into larger associations at smaller than national levels. From the earliest times, Councils of the Apostles, augmented by Bishops (sometimes called “elders”) and Presbyters (also sometimes called “elders”) might meet (as documented in Acts) and make decisions about the affected congregations, but there was really never a strong central government. That all changed in 325, when the then Emperor, Constantine the Great, legalized the Church and made it part of the government of the Roman Empire. From that time on, Bishops had large geographic responsibilities and local congregations occupied a “parish”. From 325 until 750 or so, this was the new model: The emperor in charge, with three, then four, then five Patriarchs assisting him. The Patriarchs were in Rome, Constantinople, Alexandria, Jerusalem and Antioch. After 750, though, Jerusalem, Antioch and Alexandria had all been taken over by Islam. The Churches there continued for another thousand years (indeed, they’re still there, today), but they were never a part of the “one” Church, after that. Neither was the Nestorian Church, further east.
After 750 too, Rome and Constantinople drifted even further apart. The Eastern Roman Empire, by this time being called “Byzantine” continued until it was finally overrun by the Turks in 1453, and the Patriarch was always under the control of the emperor. In Rome though, there was no effective “empire” after 476, so the Patriarch (by then being called “the Pope” ended up taking over most of the functions of civil government. On Christmas Day in the year 800, the king of France, Charles the Great, was kneeling in what then passed as St. Peter’s in Rome, and the Pope, Leo III suddenly and without much ado, placed a golden crown on his head. The Roman citizens standing around proclaimed him “Emperor” of Rome. The actual Emperor, still sitting in Constantinople, was not impressed, but there was nothing he could do about it. There had, after all, been separate “emperors” in the two halves of the Empire on and off for many years. It did cause a good deal of discordance between the two wings of the Church, though.
Two hundred years later, that discordance reached a peak when the two Patriarchs excommunicated each other in 1054. Until that time, there had been many Eastern Rite Churches in Italy and the West, and a good many Roman Rite Churches in Greece and the East. From 1054 until Constantinople fell to the Turks in 1453, the two halves of Christendom might as well have been separate Churches.