demonstrate vs testify

demonstrate and testify both are verbs.

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

As verbs, testify is a hypernym of demonstrate; that is, testify 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
testify: provide evidence for

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

demonstrate (verb)	testify (verb)
establish the validity of something, as by an example, explanation or experiment	give testimony in a court of law
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
march in protest; take part in a demonstration