support vs show

support and show both are nouns.

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

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

support: establish or strengthen as with new evidence or facts
show: establish the validity of something, as by an example, explanation or experiment

Other hyponyms of support include back, back up, vouch, verify, demonstrate, establish, prove, shew, document, validate.

support (noun)	show (noun)
aiding the cause or policy or interests of	an act or social event involving a public performance or entertainment
the act of bearing the weight of or strengthening	pretending that something is the case in order to make a good impression
documentary validation	something intended to communicate a particular impression
a military operation (often involving new supplies of men and materiel) to strengthen a military force or aid in the performance of its mission
the activity of providing for or maintaining by supplying with money or necessities
any device that bears the weight of another thing
supporting structure that holds up or provides a foundation
something providing immaterial assistance to a person or cause or interest
a musical part (vocal or instrumental) that supports or provides background for other musical parts
the financial means whereby one lives
financial resources provided to make some project possible

support (verb)	show (verb)
establish or strengthen as with new evidence or facts	establish the validity of something, as by an example, explanation or experiment
put up with something or somebody unpleasant	provide evidence for
adopt as a belief	indicate a place, direction, person, or thing; either spatially or figuratively
argue or speak in defense of	give expression to
be a regular customer or client of	give evidence of, as of records
be the physical support of; carry the weight of	indicate a certain reading; of gauges and instruments
play a subordinate role to (another performer)	finish third or better in a horse or dog race
support materially or financially	show in, or as in, a picture
give moral or psychological support, aid, or courage to	take (someone) to their seats, as in theaters or auditoriums
be behind; approve of	make visible or noticeable
support with evidence or authority or make more certain or confirm	be or become visible or noticeable
	give an exhibition of to an interested audience