drag one's heels vs delay

drag one's heels is not a noun while delay is a noun.

Word	Noun	Adjective	Verb	Adverb
drag one's heels	No	No	Yes	No
delay	Yes	No	Yes	No

As verbs, delay is a hypernym of drag one's heels; that is, delay is a word with a broader meaning than drag one's heels:

drag one's heels (noun)	delay (noun)
	the act of delaying; inactivity resulting in something being put off until a later time
	time during which some action is awaited

drag one's heels (verb)	delay (verb)
postpone doing what one should be doing	cause to be slowed down or delayed
	stop or halt
	slow the growth or development of
	act later than planned, scheduled, or required