fall back vs relapse

fall back is not a noun while relapse is a noun.

Word	Noun	Adjective	Verb	Adverb
fall back	No	No	Yes	No
relapse	Yes	No	Yes	No

As verbs, fall back and relapse are synonyms defined as:

Other synonyms of fall back include lapse, recidivate, regress, retrogress.

fall back (noun)	relapse (noun)
	a failure to maintain a higher state

fall back (verb)	relapse (verb)
go back to bad behavior	go back to bad behavior
retreat	deteriorate in health
hang (back) or fall (behind) in movement, progress, development, etc.
fall backwards and down
move back and away from
have recourse to