come out vs happen

come out and happen both are verbs.

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

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

Other hypernyms of come out include materialise, materialize.

come out (verb)	happen (verb)
appear or become visible; make a showing	come to pass
be issued or published	come into being; become reality
break out	happen, occur, or be the case in the course of events or by chance
come out of	come upon, as if by accident; meet with
take a place in a competition; often followed by an ordinal	chance to be or do something, without intention or causation
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