back off vs pull out

back off and pull out both are verbs.

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

As verbs, back off and pull out are synonyms defined as:

Other synonyms of back off include back down, bow out, chicken out.

back off (verb)	pull out (verb)
move backwards from a certain position	remove, usually with some force or effort; also used in an abstract sense
remove oneself from an obligation	move out or away
	bring, take, or pull out of a container or from under a cover
	remove oneself from an obligation