right wing vs faction

right wing and faction both are nouns.

Word	Noun	Adjective	Verb	Adverb
right wing	Yes	No	No	No
faction	Yes	No	No	No

As nouns, faction is a hypernym of right wing; that is, faction is a word with a broader meaning than right wing:

right wing: those who support political or social or economic conservatism; those who believe that things are better left unchanged
faction: a dissenting clique

Other hypernyms of right wing include sect.

right wing (noun)	faction (noun)
those who support political or social or economic conservatism; those who believe that things are better left unchanged	a dissenting clique
	a clique (often secret) that seeks power usually through intrigue