Roman Church vs Catholic Church

Roman Church and Catholic Church both are nouns.

Word	Noun	Adjective	Verb	Adverb
Roman Church	Yes	No	No	No
Catholic Church	Yes	No	No	No

As nouns, Catholic Church is a hypernym of Roman Church; that is, Catholic Church is a word with a broader meaning than Roman Church:

Roman Church: the Christian Church based in the Vatican and presided over by a pope and an episcopal hierarchy
Catholic Church: any of several churches claiming to have maintained historical continuity with the original Christian Church

Roman Church (noun)	Catholic Church (noun)
the Christian Church based in the Vatican and presided over by a pope and an episcopal hierarchy	any of several churches claiming to have maintained historical continuity with the original Christian Church