Catholic church and Roman Church

Catholic church noun - Any of several churches claiming to have maintained historical continuity with the original Christian Church.

Roman Church and Catholic church are semantically related. In some cases you can replace phrase "Roman Church" with "Catholic church", this phrases are similar.

Roman Church noun - The Christian Church based in the Vatican and presided over by a pope and an episcopal hierarchy.

Catholic church and Roman Church are semantically related. You can use "Catholic church" instead a noun phrase "Roman Church".