back up vs pull back

back up and pull back both are verbs.

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

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

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

back up (verb)	pull back (verb)
establish as valid or genuine	make a retreat from an earlier commitment or activity
become or cause to become obstructed	move to a rearward position; pull towards the back
make a copy of (a computer file) especially for storage in another place as a security copy	stretch back a bowstring (on an archer's bow)
move backwards from a certain position	use a surgical instrument to hold open (the edges of a wound or an organ)
give moral or psychological support, aid, or courage to	pull back or move away or backward