pursue vs chase after

pursue and chase after both are verbs.

Word	Noun	Adjective	Verb	Adverb
pursue	No	No	Yes	No
chase after	No	No	Yes	No

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

Other hyponyms of pursue include stalk, chase, dog, give chase, go after, tag, tail, track, trail, haunt, stalk.

pursue (verb)	chase after (verb)
go in search of or hunt for	go after with the intent to catch
follow in or as if in pursuit	pursue someone sexually or romantically
carry out or participate in an activity; be involved in
carry further or advance