Roman vs romish

Roman is a noun but romish is not a noun.

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

As adjectives, Roman and romish are synonyms defined as:

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

Roman (noun)	romish (noun)
a resident of modern Rome
an inhabitant of the ancient Roman Empire

Roman (adjective)	romish (adjective)
of or relating to or supporting Romanism	of or relating to or supporting Romanism
of or relating to or derived from Rome (especially ancient Rome)
characteristic of the modern type that most directly represents the type used in ancient Roman inscriptions