Prior to the Great Schism, there were 5 Apostolic Patriarchates...Rome, Constantinople, Alexandria, Antioch, and Jerusalem. Each Patriarch/Pope was considered equal. But the Pope of Rome wanted to be the “first amongst equals”. The other 4 Patriarchs were not pleased with that arrangement. The churches split into the Roman/Western Catholic Church, while the other 4 patriarchates became what is considered the Eastern (Orthodox) Church.
“But the Pope of Rome wanted to be the first amongst equals. The other 4 Patriarchs were not pleased with that arrangement.”
That is correct, and that is how the term Roman Catholic started. It was western, and Latin based in Rome. It was a term used to distinguish between the western and eastern branches of the “catholic’ church.
The Patriarchate of Antioch frequently remained in communion with both Rome and Constantinople after the schism of 1054 until the formation of the Melkite Catholic Church in 1724.
The Melkites still assert patriarchal authority against the papacy today despite their union with Rome.