run down vs give chase

run down and give chase both are verbs.

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

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

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

run down (verb)	give chase (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 until captured
move downward
examine hastily
deplete
trace