protest vs demonstrate

protest is a noun but demonstrate is not a noun.

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

As verbs, demonstrate is a hyponym of protest; that is, demonstrate is a word with a more specific, narrower meaning than protest:

Other hyponyms of protest include strike, walk out, march, arise, rebel, rise, rise up, rebel, renegade.

protest (noun)	demonstrate (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)	demonstrate (verb)
utter words of protest	establish the validity of something, as by an example, explanation or experiment
affirm or avow formally or solemnly	provide evidence for; stand as proof of; show by one's behavior, attitude, or external attributes
express opposition through action or words	give an exhibition of to an interested audience
	march in protest; take part in a demonstration