move back vs back off

move back and back off both are verbs.

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

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

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

move back (verb)	back off (verb)
pull back or move away or backward	move backwards from a certain position
	remove oneself from an obligation