There are other terms that can be used depending on the specific context:
* Art song: A classical vocal piece that sets a poem to music, typically with a focus on the text and a more intimate style.
* Ballad: A song that tells a story, often with a simple melody and repetitive structure.
* Hymn: A religious song, typically with a strong, uplifting melody.
* Lullaby: A soothing song intended to calm a child.
* Opera: A theatrical work that combines music, singing, and acting.
Ultimately, the specific term used to describe a poem set to music will depend on the genre, style, and purpose of the piece.