come out vs emerge

come out and emerge both are verbs.

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

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

Other synonyms of come out include come forth, egress, go forth, issue.

As verbs, emerge is a hypernym of come out; that is, emerge is a word with a broader meaning than come out:

Other hypernyms of come out include come forth, come out, egress, go forth, issue.

come out (verb)	emerge (verb)
appear or become visible; make a showing	come out into view, as from concealment
be issued or published	become known or apparent
break out	come out of
come out of	come up to the surface of or rise
take a place in a competition; often followed by an ordinal	happen or occur as a result of something
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