pull away vs back down

pull away and back down both are verbs.

Word	Noun	Adjective	Verb	Adverb
pull away	No	No	Yes	No
back down	No	No	Yes	No

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

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

pull away (verb)	back down (verb)
pull back or move away or backward	move backwards from a certain position
	remove oneself from an obligation