Quote by Cora
It differs from poetry, which is what I seem to gravitate towards.
They are different but I think they also interact. Just look at my posts about Leonard Cohen in the poets poll thread. And it is not just him, other songwriters have also been published poets (the late Gord Downie of Canadian alt-rockers The Tragically Hip comes to mind). Most lyrics are poetry in form, but then also need to adapt to the flow of music, which is where the difference comes in. Great lyrics are usually also great poetry, and lyric poetry is a genre for a reason, but the reverse is not necessarily true.
And keep in mind that we often see ancient works as poems that were actually sung in their day. The Psalms come to mind. While there are hymns and other works that are settings of them, we often encounter many of them as readings, in spoken word rather than musical form. Greek lyric poetry is mostly like that, too.
I have contemplated songwriting as well but I am not sure how one writes lyrics without a tune and while I dearly love music, I am terrible at it from a performance standpoint. So I would likely have to take an existing melody and adapt to it unless I found someone more adept at music than I to write me a tune (though I have occasionally had tunes in my head for my poems). Someone else was musing about this in a thread somewhere on here recently as well.