move back vs fall back

move back and fall back both are verbs.

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

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

Other hyponyms of move back include retreat, retrograde, back down, back off, back up.

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