Church of Rome vs Roman Church

Church of Rome and Roman Church both are nouns.

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

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

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

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

Church of Rome (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