come up vs emerge

come up and emerge both are verbs.

Word	Noun	Adjective	Verb	Adverb
come up	No	No	Yes	No
emerge	No	No	Yes	No

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

Other hyponyms of come up include resurface, bubble up, intumesce, swell, well.

come up (verb)	emerge (verb)
result or issue	come out into view, as from concealment
start running, functioning, or operating	become known or apparent
gather or bring together	come out of
gather (money or other resources) together over time	come up to the surface of or rise
bring forth, usually something desirable	happen or occur as a result of something
come up, of celestial bodies
come to the surface
move toward, travel toward something or somebody or approach something or somebody
move upward
get something or somebody for a specific purpose
originate or come into being
be mentioned