What's the Difference between Catholic, Roman Catholic, and Eastern Catholic?
The Catholic Church calls itself simply "the Catholic Church." The word "catholic" is Greek and means "universal," so the word really means "the universal church." The term "Roman Catholic" wasn't developed by the Catholic Church itself, even though the church is governed by the bishop of Rome, the Pope. The term "Roman Catholic" is so common in English-speaking countries that even many Catholics are unaware that it isn't an official term of the Catholic Church.
Eastern Catholic Churches
Since the 1500s, some groups of churches from traditions that had broken with the Catholic church in the past (often many centuries in the past) sought to join the Catholic Church but keep their own traditions and practices. These groups were recognized as "Eastern Catholic" churches which were under the Pope's authority but maintained very different traditions and laws. The church directly under the Pope's authority is called the "Latin Church."
Originally each Eastern Catholic church was active in an area with no other Catholic churches. However, immigration has led to an overlap between Latin and Eastern churches. Eastern Catholics have their own bishops, parishes, and canon laws, and so there are times when a parish needs to note the specific church a person belongs to.