show vs prove

show is a noun but prove is not a noun.

Word	Noun	Adjective	Verb	Adverb
show	Yes	No	Yes	No
prove	No	No	Yes	No

As verbs, show and prove are synonyms defined as:

show and prove: establish the validity of something, as by an example, explanation or experiment

Other synonyms of show include demonstrate, establish, shew.

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

show: establish the validity of something, as by an example, explanation or experiment
prove: prove formally; demonstrate by a mathematical, formal proof

Other hyponyms of show include prove oneself, contradict, negate, stultify.

As verbs, show and prove are synonyms defined as:

Other synonyms of show include bear witness, evidence, testify.

show (noun)	prove (noun)
an act or social event involving a public performance or entertainment
pretending that something is the case in order to make a good impression
something intended to communicate a particular impression

show (verb)	prove (verb)
establish the validity of something, as by an example, explanation or experiment	establish the validity of something, as by an example, explanation or experiment
provide evidence for	obtain probate of
indicate a place, direction, person, or thing; either spatially or figuratively	prove formally; demonstrate by a mathematical, formal proof
give expression to	provide evidence for
give evidence of, as of records	take a trial impression of
indicate a certain reading; of gauges and instruments	cause to puff up with a leaven
finish third or better in a horse or dog race	increase in volume
show in, or as in, a picture	put to the test, as for its quality, or give experimental use to
take (someone) to their seats, as in theaters or auditoriums	be shown or be found to be
make visible or noticeable
be or become visible or noticeable
give an exhibition of to an interested audience