decline vs go down

decline is a noun but go down is not a noun.

Word	Noun	Adjective	Verb	Adverb
decline	Yes	No	Yes	No
go down	No	No	Yes	No

As verbs, decline and go down are synonyms defined as:

Other synonyms of decline include wane.

As verbs, go down is a hypernym of decline; that is, go down is a word with a broader meaning than decline:

Other hypernyms of decline include come down, descend, fall.

decline (noun)	go down (noun)
a downward slope or bend
a gradual decrease; as of stored charge or current
change toward something smaller or lower
a condition inferior to an earlier condition; a gradual falling off from a better state; decline

decline (verb)	go down (verb)
grow smaller	grow smaller
grow worse	stop operating
show unwillingness towards	be defeated
inflect for number, gender, case, etc.	be ingested
go down	go under
fall in value	disappear beyond the horizon
not accept as true	move downward and lower, but not necessarily all the way
	be recorded or remembered