fake vs feign

fake is a noun but feign is not a noun.

Word	Noun	Adjective	Verb	Adverb
fake	Yes	Yes	Yes	No
feign	No	No	Yes	No

As verbs, feign is a hypernym of fake; that is, feign is a word with a broader meaning than fake:

Other hypernyms of fake include affect, dissemble, pretend, sham.

fake (noun)	feign (noun)
(football) a deceptive move made by a football player
something that is a counterfeit; not what it seems to be
a person who makes deceitful pretenses

fake (adjective)	feign (adjective)
not genuine or real; being an imitation of the genuine article
fraudulent; having a misleading appearance

fake (verb)	feign (verb)
speak insincerely or without regard for facts or truths	make believe with the intent to deceive
make a copy of with the intent to deceive	make a pretence of
tamper, with the purpose of deception