verse vs poem

verse and poem both are nouns.

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

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

Other hypernyms of verse include verse form.

verse (noun)	poem (noun)
a piece of poetry	a composition written in metrical feet forming rhythmical lines
a line of metrical text
literature in metrical form

verse (verb)	poem (verb)
familiarize through thorough study or experience
compose verses or put into verse