Roman Church vs Church of Rome

Roman Church and Church of Rome both are nouns.

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

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

Roman Church 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 Church include Roman Catholic, Roman Catholic Church, Western Church.

Roman Church (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