leftist vs left-wing

leftist is a noun but left-wing is not a noun.

Word	Noun	Adjective	Verb	Adverb
leftist	Yes	Yes	No	No
left-wing	No	Yes	No	No

As adjectives, leftist and left-wing are synonyms defined as:

leftist and left-wing: believing in or supporting tenets of the political left

Other synonyms of leftist include left-of-center.

leftist (noun)	left-wing (noun)
a person who belongs to the political left

leftist (adjective)	left-wing (adjective)
believing in or supporting tenets of the political left	believing in or supporting tenets of the political left