Roman Church vs Roman Catholic

Roman Church and Roman Catholic both are nouns.

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

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

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

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

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