go on vs run on

go on and run on both are verbs.

Word	Noun	Adjective	Verb	Adverb
go on	No	No	Yes	No
run on	No	No	Yes	No

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

Other hyponyms of go on include hold, keep going, ride.

go on (verb)	run on (verb)
come to pass	talk or narrate at length
continue talking	continue uninterrupted
start running, functioning, or operating
move forward, also in the metaphorical sense
continue a certain state, condition, or activity