protest vs complain

protest is a noun but complain is not a noun.

Word	Noun	Adjective	Verb	Adverb
protest	Yes	No	Yes	No
complain	No	No	Yes	No

As verbs, complain is a hypernym of protest; that is, complain is a word with a broader meaning than protest:

Other hypernyms of protest include kick, kvetch, plain, quetch, sound off.

protest (noun)	complain (noun)
the act of protesting; a public (often organized) manifestation of dissent
a formal and solemn declaration of objection
the act of making a strong public expression of disagreement and disapproval

protest (verb)	complain (verb)
utter words of protest	express complaints, discontent, displeasure, or unhappiness
affirm or avow formally or solemnly	make a formal accusation; bring a formal charge
express opposition through action or words