right-wing vs rightist

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

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

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

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

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

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