back up vs move back

back up and move back both are verbs.

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

As verbs, move back is a hypernym of back up; that is, move back is a word with a broader meaning than back up:

Other hypernyms of back up include draw back, pull away, pull back, recede, retire, retreat, withdraw.

back up (verb)	move back (verb)
establish as valid or genuine	pull back or move away or backward
become or cause to become obstructed
make a copy of (a computer file) especially for storage in another place as a security copy
move backwards from a certain position
give moral or psychological support, aid, or courage to