come up vs become

come up and become both are verbs.

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

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

come up (verb)	become (verb)
result or issue	enter or assume a certain state or condition
start running, functioning, or operating	come into existence
gather or bring together	undergo a change or development
gather (money or other resources) together over time	enhance the appearance of
bring forth, usually something desirable
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