come out vs egress

come out is not a noun while egress is a noun.

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

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

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

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

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

come out (noun)	egress (noun)
	the act of coming (or going) out; becoming apparent
	(astronomy) the reappearance of a celestial body after an eclipse
	the becoming visible

come out (verb)	egress (verb)
appear or become visible; make a showing	come out of
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