trail vs chase after

trail is a noun but chase after is not a noun.

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

As verbs, trail and chase after are synonyms defined as:

Other synonyms of trail include chase, dog, give chase, go after, tag, tail, track.

trail (noun)	chase after (noun)
a path or track roughly blazed through wild or hilly country
evidence pointing to a possible solution
a track or mark left by something that has passed

trail (verb)	chase after (verb)
drag loosely along a surface; allow to sweep the ground	go after with the intent to catch
hang down so as to drag along the ground	pursue someone sexually or romantically
go after with the intent to catch
move, proceed, or walk draggingly or slowly
to lag or linger behind