The Catholic Church has had several Eastern Rites for most of
her history. In the eleventh century, most of the Eastern Rites
split in two, which half of each Rite remained with the church and
half forming the new Orthodox Church. Thus the Greek Orthodox
Church has the same liturgy as the Greek Uniate Church, but they
are no longer in communion with Rome. Nearly all of the Eastern
Rites did this, although I do not think that there is a "Russian"
Uniate Church. Anyway, all of the Orthodox Churches are not in
union with Rome.