back off vs bow out

back off and bow out both are verbs.

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

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

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

back off (verb)	bow out (verb)
move backwards from a certain position	retire gracefully
remove oneself from an obligation	remove oneself from an obligation