Roman Catholic vs Church of Rome

Roman Catholic and Church of Rome both are nouns.

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

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

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

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

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