come out vs pop out

come out and pop out both are verbs.

Word	Noun	Adjective	Verb	Adverb
come out	No	No	Yes	No
pop out	No	No	Yes	No

As verbs, pop out is a hyponym of come out; that is, pop out is a word with a more specific, narrower meaning than come out:

Other hyponyms of come out include radiate, leak, escape, fall, debouch, come out, fall out.

As verbs, come out and pop out are synonyms defined as:

Other synonyms of come out include bug out, bulge, bulge out, pop, protrude, start.

come out (verb)	pop out (verb)
appear or become visible; make a showing	come out suddenly or forcefully
be issued or published	exit briefly
break out	bulge outward
come out of	appear suddenly or unexpectedly; happen unexpectedly
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