draw back vs back down

draw back and back down both are verbs.

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

As verbs, back down is a hyponym of draw back; that is, back down is a word with a more specific, narrower meaning than draw back:

Other hyponyms of draw back include fall back, retreat, retrograde, back off, back up.

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