come out vs show up

come out and show up both are verbs.

Word	Noun	Adjective	Verb	Adverb
come out	No	No	Yes	No
show up	No	No	Yes	No

As verbs, come out and show up are synonyms defined as:

Other synonyms of come out include come on, surface, turn up.

come out (verb)	show up (verb)
appear or become visible; make a showing	appear or become visible; make a showing
be issued or published	be or become visible or noticeable
break out
come out of
take a place in a competition; often followed by an ordinal
be made known; be disclosed or revealed
to state openly and publicly one's homosexuality
bulge outward
make oneself visible; take action
drop out
result or end