A point of vocabulary when referring to Eastern Catholics. The Eastern Churches in full union with Rome are not referred to as Roman Catholic. They may be referred to by their proper name, such as, Melkite Catholic Church. Additionally, a "rite" is not the same as a "Church." There are about 10 (depending on how one counts) ritual families in the Catholic Church. However, there are 22 Churches that comprise the Catholic Church. Many Eastern Catholic Churches share the same rite, such as the Ukrainian Catholic Church and the Romanian Catholic Church. Some Churches, like the Chaldean Catholic Church share the same rite as another Church not in full union with Rome (in this case, the Assyrian Church of the East.)
Eastern Churches in full union with Rome have their own Canon Law, ritual traditions, their own autonomous hierarchy and they govern their own internal affairs. Roman Catholics, properly referred, are those Westerns that belong to the Roman (or Latin) Church. Together, Latins and Easterns in full union with Rome comprise the Catholic Church.
This union in no way impugnes the distinctive dignity of the Oriental Orthodox Church, Eastern Orthodox Church or the Assyrian Church of the East.