Roman Catholic church is the largest in the Latin rite. For example until relatively lately the Gaelic (Irish) church, though of the Latin rite was separate from the Roman catholics.. Same in the east. Though they are catholic they are far from Roman catholics. These include Byzantine, Ruthenian, Ukrainian, Coptic, Maronite, and several others. On the surface they may look like Orthodox (as JP2 referred to as the 'other lung') but are traditional catholics. All have a patriarch who is the liaison between the people and the pope. If a pope makes a claim that the patriarch finds is against catholic doctrine, he advises the people they need not comply. For example, everything that occurred from Vatican II did not impact any of the churches in the Eastern Rite. In the East there is no novus ordo (new order) masses; they are relatively unchanged thru out t=its time.

All that you hear about pedo priests,etc if you check into it, is only Roman catholics, Eastern Rite is traditional with pretty strict rules such as in this case they cannot go anywhere without someone else accompanying them.