evidence vs demonstrate

evidence is a noun but demonstrate is not a noun.

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

As verbs, evidence and demonstrate are synonyms defined as:

evidence and demonstrate: provide evidence for; stand as proof of; show by one's behavior, attitude, or external attributes

Other synonyms of evidence include attest, certify, manifest.

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

evidence: provide evidence for
demonstrate: provide evidence for; stand as proof of; show by one's behavior, attitude, or external attributes

Other hyponyms of evidence include attest, certify, evidence, manifest, presume, abduce, adduce, cite.

evidence (noun)	demonstrate (noun)
your basis for belief or disbelief; knowledge on which to base belief
(law) all the means by which any alleged matter of fact whose truth is investigated at judicial trial is established or disproved
an indication that makes something evident

evidence (verb)	demonstrate (verb)
provide evidence for; stand as proof of; show by one's behavior, attitude, or external attributes	establish the validity of something, as by an example, explanation or experiment
provide evidence for	provide evidence for; stand as proof of; show by one's behavior, attitude, or external attributes
give evidence	give an exhibition of to an interested audience
	march in protest; take part in a demonstration