demonstrate vs evidence

demonstrate is not a noun while evidence is a noun.

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

As verbs, demonstrate and evidence are synonyms defined as:

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

Other synonyms of demonstrate include attest, certify, manifest.

As verbs, evidence is a hypernym of demonstrate; that is, evidence is a word with a broader meaning than demonstrate:

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

Other hypernyms of demonstrate include bear witness, prove, show, testify.

demonstrate (noun)	evidence (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

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