testify vs demonstrate

testify and demonstrate both are verbs.

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

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

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

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

testify (verb)	demonstrate (verb)
give testimony in a court of law	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 an exhibition of to an interested audience
	march in protest; take part in a demonstration