Roman Catholic vs Roman Church

Roman Catholic and Roman Church both are nouns.

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

As nouns, Roman Catholic and Roman Church are synonyms defined as:

Roman Catholic and Roman Church: the Christian Church based in the Vatican and presided over by a pope and an episcopal hierarchy

Other synonyms of Roman Catholic include Church of Rome, Roman Catholic Church, Western Church.

Roman Catholic (noun)	Roman Church (noun)
the Christian Church based in the Vatican and presided over by a pope and an episcopal hierarchy	the Christian Church based in the Vatican and presided over by a pope and an episcopal hierarchy
a member of the Roman Catholic Church

Roman Catholic (adjective)	Roman Church (adjective)
of or relating to or supporting Romanism