regress vs fall back

regress is a noun but fall back is not a noun.

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

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

Other synonyms of regress include lapse, recidivate, relapse, retrogress.

As verbs, fall back is a hyponym of regress; that is, fall back is a word with a more specific, narrower meaning than regress:

Other hyponyms of regress include drop off, fall behind, recede.

As verbs, fall back is a hyponym of regress; that is, fall back is a word with a more specific, narrower meaning than regress:

Other hyponyms of regress include lapse, recidivate, regress, relapse, retrogress, resile, go back, recover, recuperate.

regress (noun)	fall back (noun)
returning to a former state
the reasoning involved when you assume the conclusion is true and reason backward to the evidence

regress (verb)	fall back (verb)
go back to bad behavior	go back to bad behavior
get worse or fall back to a previous condition	retreat
go back to a previous state	hang (back) or fall (behind) in movement, progress, development, etc.
go back to a statistical means	fall backwards and down
	move back and away from
	have recourse to