bow out vs back down

bow out and back down both are verbs.

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

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

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

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