come out vs break through

come out and break through both are verbs.

Word	Noun	Adjective	Verb	Adverb
come out	No	No	Yes	No
break through	No	No	Yes	No

As verbs, come out and break through are synonyms defined as:

Other synonyms of come out include erupt, push through.

come out (verb)	break through (verb)
appear or become visible; make a showing	penetrate
be issued or published	break out
break out	pass through (a barrier)
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