Laurasia, welcome to the boards.
Just so you are aware, there are two meanings to the "Catholic Church"; it is both visible and invisible.
The Visible Catholic Church: The visible confines of the Catholic Church is based in Rome, and as mentioned above, anyone who is part of the visible Catholic Church ultimately submits to the authority of the Bishop of Rome (the pope); this includes the Eastern Rites, as mentioned above, but not the Orthodox, Anglicans, Lutherans, etc.
The Invisible Catholic Church: The invisible Catholic Church is the mystical bride of Christ, which is united with Christ as His body. People who are part of the body of Christ are basically anyone who has surrendered their lives to Christ. This can include those who are not part of the visible Catholic Church, like the Orthodox, Baptists, Lutherans, Anglicans, etc. yet they are imperfectly united to the visible Church.
Also, some Catholics take offense to the term "Roman Catholic", because aparently the word "Roman" was tagged on originally as an insult and a means of dvision. When someone says "Catholic", it usually means they submit to the pope, so the "Roman" tag is not really needed.
Hope this helps. And, welcome to the family.
May the Lord give you His peace!
-Davide