move up vs come up

move up and come up both are verbs.

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

As verbs, move up and come up are synonyms defined as:

Other synonyms of move up include arise, go up, lift, rise, uprise.

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

move up (verb)	come up (verb)
move upward	result or issue
move to a better position in life or to a better job	start running, functioning, or operating
	gather or bring together
	gather (money or other resources) together over time
	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