get going vs come up

get going and come up both are verbs.

Word	Noun	Adjective	Verb	Adverb
get going	No	No	Yes	No
come up	No	No	Yes	No

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

Other hyponyms of get going include come on, go on, get off the ground, take off.

get going (verb)	come up (verb)
start to be active	result or issue
begin or set in motion	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