pull back vs back up

pull back and back up both are verbs.

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

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

Other hyponyms of pull back include fall back, retreat, retrograde, back down, back off.

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