rightist vs right-wing

rightist is a noun but right-wing is not a noun.

Word	Noun	Adjective	Verb	Adverb
rightist	Yes	Yes	No	No
right-wing	No	Yes	No	No

As adjectives, rightist and right-wing are synonyms defined as:

rightist and right-wing: believing in or supporting tenets of the political right

rightist (noun)	right-wing (noun)
a member of a right wing political party

rightist (adjective)	right-wing (adjective)
believing in or supporting tenets of the political right	believing in or supporting tenets of the political right