Where verse is set to music, the distinction between poem and song may become artificial. This is perhaps recognised in the way popular songs have lyrics: so see list of songs by name. The verse, however, may precede the tune (in the way that Rule Britannia was set to music, and And did those feet in ancient time has become the hymn Jerusalem); the tune may be lost over time but the words survive; a number of alternate tunes may fit (for some hymns and ballads this is commonly seen). Possible classifications proliferate (under anthem, ballad, blues, carol, folk song, hymn, libretto, lied, lullaby, march, praise song, spiritual). Nursery rhymes may be songs, or doggerel: the term doesn't imply a distinction. See rap, roots of rap music also, on the boundaries: verse+music against verse against verse set to music.
Verse drama might normally be judged (at its best) as poetry, but not consisting of poems. Again there are genres as far apart as masque and pantomime.
See anyway:-