Roman Catholic vs romish

Roman Catholic is a noun but romish is not a noun.

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

As adjectives, Roman Catholic and romish are synonyms defined as:

Other synonyms of Roman Catholic include papist, papistic, papistical, popish, R.C., Roman, Romanist.

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