run down vs chase after

run down and chase after both are verbs.

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

As verbs, chase after is a hypernym of run down; that is, chase after is a word with a broader meaning than run down:

Other hypernyms of run down include chase, dog, give chase, go after, tag, tail, track, trail.

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