back off vs pull back

back off and pull back both are verbs.

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

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

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

back off (verb)	pull back (verb)
move backwards from a certain position	make a retreat from an earlier commitment or activity
remove oneself from an obligation	move to a rearward position; pull towards the back
	stretch back a bowstring (on an archer's bow)
	use a surgical instrument to hold open (the edges of a wound or an organ)
	pull back or move away or backward