fall away vs decline

fall away is not a noun while decline is a noun.

Word	Noun	Adjective	Verb	Adverb
fall away	No	No	Yes	No
decline	Yes	No	Yes	No

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

Other hypernyms of fall away include worsen.

fall away (noun)	decline (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

fall away (verb)	decline (verb)
fall to a lower standard	grow smaller
diminish in size or intensity	grow worse
	show unwillingness towards
	inflect for number, gender, case, etc.
	go down
	fall in value
	not accept as true