chase after vs run down

chase after and run down both are verbs.

Word	Noun	Adjective	Verb	Adverb
chase after	No	No	Yes	No
run down	No	No	Yes	No

As verbs, run down is a hyponym of chase after; that is, run down is a word with a more specific, narrower meaning than chase after:

Other hyponyms of chase after include tree, quest, hound, hunt, trace.

chase after (verb)	run down (verb)
go after with the intent to catch	use up all one's strength and energy and stop working
pursue someone sexually or romantically	injure or kill by knocking (someone or something) down and passing over the body, as with a vehicle
	pursue until captured
	move downward
	examine hastily
	deplete
	trace