put back vs lay

put back is not a noun while lay is a noun.

Word	Noun	Adjective	Verb	Adverb
put back	No	No	Yes	No
lay	Yes	Yes	Yes	No

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

Other hypernyms of put back include place, pose, position, put, set.

put back (noun)	lay (noun)
	a narrative poem of popular origin
	a narrative song with a recurrent refrain

put back (adjective)	lay (adjective)
	not of or from a profession
	characteristic of those who are not members of the clergy

put back (verb)	lay (verb)
put something back where it belongs	put in a horizontal position
cost a certain amount	put into a certain place or abstract location
	lay eggs
	prepare or position for action or operation
	impose as a duty, burden, or punishment