How is a song lyric different from a poem?

How is a song lyric different from a poem?  It's a question that I get asked a lot but up to now I've never been able to come up with a satisfactory answer.

However, just recently I've been looking back at some of the libretti that I've written  for my old friend, composer Roderick Skeaping and it suddenly struck me where there might be an answer.

In a play there has to be an internal logic; a style, a consistent voice, a set of conventions, a unity that holds the whole thing together.  Everything has to fall within this reality even if I am writing a complete fantasy set in a fantasy world in some far off galaxy.  The point is, that whatever the convention I decide upon, I have to stick within it.  People soon feel uncomfortable if the playwright moves outside the strict limits that have been set from page one.  In other words, if there are two moons in the sky and green aliens, I must ensure that I don't suddenly have three moons and purple aliens.
However, this ceases to be the case with a libretto.  The writer is suddenly free of such restrictions.  We can move from one moment seeing the world through one set of eyes to another quite different.  It is the music that provides the logic.  That is convention that binds together all the free floating ideas and images, first in one voice and then in another.  We are not bound by unity of time and space in quite the way we are in a stage play where logic comes from real dialogue in real time.
Now apply this idea to poetry and song writing.  A poem must have a structure that lures the listener or reader through the piece.  The words are paramount.  There is nothing else.  With a lyric, however, we have the music to draw us through the piece so that our ideas can range here and there, reaching out to pull in images from many sources.  In fact, the less internal logic there is in a lyric, the better the song.
I was writing a set of songs for a play with Roddy composing the music.  Most of the songs I had carefully crafted beforehand, making sure every word was perfectly polished.  But there was one song I was having difficulty with.  All I had for this was some scribbled notes on the back of an old Tesco's receipt.  Roddy propped the receipt on the piano and began to improvise.  With almost no alteration it turned out to be the most satisfactory song of the piece.