run on vs continue

run on and continue both are verbs.

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

As verbs, continue is a hypernym of run on; that is, continue is a word with a broader meaning than run on:

Other hypernyms of run on include go along, go on, keep, proceed.

run on (verb)	continue (verb)
talk or narrate at length	exist over a prolonged period of time
continue uninterrupted	continue talking
	move ahead; travel onward in time or space
	allow to remain in a place or position or maintain a property or feature
	keep or maintain in unaltered condition; cause to remain or last
	continue a certain state, condition, or activity
	span an interval of distance, space or time
	continue in a place, position, or situation
	continue after an interruption
	do something repeatedly and showing no intention to stop