come out vs fall out

come out and fall out both are verbs.

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

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

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

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

come out (verb)	fall out (verb)
appear or become visible; make a showing	come to pass
be issued or published	have a breach in relations
break out	drop out
come out of	leave (a barracks) in order to take a place in a military formation, or leave a military formation
take a place in a competition; often followed by an ordinal	come as a logical consequence; follow logically
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