There seems to be much confusion as of late with regard to Eastern Catholicism and it’s place within the Catholic Church. Some have expressed doubts with regard to the fullness of the Eastern Catholic Churches’ communion with Rome, especially in light of the Eastern Catholics’ differences in liturgy and theological perspective when compared to those of the (vastly larger) Latin Church.
Most Eastern Catholics today owe their Catholicism to one of two treaties enacted many years ago. The Ukranian Byzantine Catholics officially reunited with Rome in 1595, via the Treaty of Brest; the Ruthenian Byzantine Catholics reunited roughly 50 years later, in 1646, via the Treaty of Uzhorod. These two treaties spelled out the terms under which the reunification with Rome would be affected, and were agreed to by both Rome and the particular Eastern Church seeking reunification.
…spells out the terms of reunification as set forth in the Treaty of Brest with regard to the Ukranian Byzantine Catholic Church (referred to back then as the Greek Catholic Church); the terms implicit in the Treaty of Uzhorod affecting the Ruthenian Byzantine Catholic Church are virtually identical.
These treaties are still in effect today. In fact, our Holy Father has recently referenced the terms contained in these documents, and has mandated that all Catholics should be aware of these terms and should take whatever steps necessary to ensure that the Eastern Catholic Churches be allowed to return as much as possible to the liturgical and theological guarantees spelled out in these agreements in order to wipe away the vestiges of “Latinization” that have crept into the Eastern Churches over the centuries.
Please take a moment to read the document in the above link. Hopefully it will shed some light on how we came to be many “Churches” with many liturgical practices, yet all united in our Catholicity under our Holy Father, the Pope of Rome.