lay vs poem

lay and poem both are nouns.

Word	Noun	Adjective	Verb	Adverb
lay	Yes	Yes	Yes	No
poem	Yes	No	No	No

As nouns, poem is a hypernym of lay; that is, poem is a word with a broader meaning than lay:

Other hypernyms of lay include verse form.

lay (noun)	poem (noun)
a narrative poem of popular origin	a composition written in metrical feet forming rhythmical lines
a narrative song with a recurrent refrain

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

lay (verb)	poem (verb)
put in a horizontal position
put into a certain place or abstract location
lay eggs
prepare or position for action or operation
impose as a duty, burden, or punishment