set down vs lay

set down is not a noun while lay is a noun.

Word	Noun	Adjective	Verb	Adverb
set down	No	No	Yes	No
lay	Yes	Yes	Yes	No

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

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

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

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

set down (noun)	lay (noun)
	a narrative poem of popular origin
	a narrative song with a recurrent refrain

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

set down (verb)	lay (verb)
put down in writing; of texts, musical compositions, etc.	put in a horizontal position
remove (cargo, people, etc.) from and leave	put into a certain place or abstract location
put or settle into a position	lay eggs
cause to sit or seat or be in a settled position or place	prepare or position for action or operation
go ashore	impose as a duty, burden, or punishment
reach or come to rest