I usually tell my students that while most poetry could become song lyrics, not all song lyrics are poetry.

Poetry, by itself (like music) is supposed to auditory - meaning, a form of writing that is meant to be heard.  This is why we recommend poetry be read aloud.  Sound elements in poetry include: rhythm, rhyme, alliteration, assonance, repetition, even refrain.

Just as in music the instruments and beat can help create emotion - poetry can be written in a way that the rhythm and movement add to the emotion.  While prose tends to be more formal and often more straight forward - poetry is whimsical - less formal - what is left out of the words is often added through the sound elements.  Often the feelings provided by the sound elements make the words more meaningful.

First of all, songs and poetry are forms of art and a way to express creativity. Both songs and poetry are also ways that people express themselves or convey feelings, thoughts, dreams, fears, emotions, etc. I think that this is how they are related. In addition, there are many elements of poetry that are in songs. For example, they both have rhythm. The difference between the two is that songs are put to music, although many poems have been put to music.

I have posted a link below that contains some really good information on music and poetry and how they are related.