The prefix Roman distinguishes it from other Catholic churches, but it is not correct to say that this excludes
Protestant churches. The
Church of England is known as the
Holy,
Catholic, and
Apostolic Church of England.
I would suggest that a Catholic church is (roughly) one that accepts the Nicene Creed with the filioque, and believes in the apostolic succession.
(Later: isido, who seems to know a whole lot better than me (see Orthodox Christian) says it isn't that simple, and I'm sure it isn't. I don't know enough about Eastern Catholicism, and hope that isido or someone will write up the details.)
The Roman Catholic Church dislike the prefix 'Roman' because it smacks of those old Protestant terms of disparagement, like 'Romish' and 'popish' and 'papist'. So they (I am told) prefer to call themselves the Catholic Church. However, this is begging the question: the Pope claims to be head of all of the Catholic church, but other Catholic churches (such as the Church of England) firmly deny that he is. According to them, he is the Bishop of Rome and heads only the Roman branch of the church, and those Eastern ones in communion with it.