back down vs draw back

back down and draw back both are verbs.

Word	Noun	Adjective	Verb	Adverb
back down	No	No	Yes	No
draw back	No	No	Yes	No

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

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

back down (verb)	draw back (verb)
move backwards from a certain position	use a surgical instrument to hold open (the edges of a wound or an organ)
remove oneself from an obligation	pull back or move away or backward