decline vs turn down

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

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

As verbs, turn down is a hyponym of decline; that is, turn down is a word with a more specific, narrower meaning than decline:

As verbs, turn down is a hyponym of decline; that is, turn down is a word with a more specific, narrower meaning than decline:

Other hyponyms of decline include disdain, freeze off, pooh-pooh, reject, scorn, spurn, contract out, regret, repudiate, disobey.

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

Other synonyms of decline include pass up, refuse, reject.

decline (noun)	turn 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)	turn down (verb)
grow smaller	make lower or quieter
grow worse	take a downward direction
show unwillingness towards	reject with contempt
inflect for number, gender, case, etc.	not accept as true
go down	refuse entrance or membership
fall in value
not accept as true