continue vs run on

continue and run on both are verbs.

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

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

Other hyponyms of continue include hold, keep going, ride.

continue (verb)	run on (verb)
exist over a prolonged period of time	talk or narrate at length
continue talking	continue uninterrupted
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