come out vs come out of the closet

come out and come out of the closet both are verbs.

Word	Noun	Adjective	Verb	Adverb
come out	No	No	Yes	No
come out of the closet	No	No	Yes	No

As verbs, come out and come out of the closet are synonyms defined as:

come out and come out of the closet: to state openly and publicly one's homosexuality

Other synonyms of come out include out.

come out (verb)	come out of the closet (verb)
appear or become visible; make a showing	to state openly and publicly one's homosexuality
be issued or published
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