seek vs go after

seek is a noun but go after is not a noun.

Word	Noun	Adjective	Verb	Adverb
seek	Yes	No	Yes	No
go after	No	No	Yes	No

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

seek (noun)	go after (noun)
the movement of a read/write head to a specific data track on a disk

seek (verb)	go after (verb)
inquire for	go in search of or hunt for
try to locate or discover, or try to establish the existence of	go after with the intent to catch
go to or towards
try to get or reach
make an effort or attempt