get going vs go on

get going and go on both are verbs.

Word	Noun	Adjective	Verb	Adverb
get going	No	No	Yes	No
go on	No	No	Yes	No

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

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

get going (verb)	go on (verb)
start to be active	come to pass
begin or set in motion	continue talking
	start running, functioning, or operating
	move forward, also in the metaphorical sense
	continue a certain state, condition, or activity