As a trad-based songwriter, I have struggled to come up with a description for what I do as opposed to the navel-gazers and diary-writers - "Literary Songwriter". Here is the description from my website:
What's a "Literary Songwriter"?
This is a term I came up with quite accidentally during a conversation where I was asked what kind of songs I write. Literary songs are tradition-based and have a definite beginning, middle and end. They often make use of literary devices like rhyme and scansion. A literary songwriter's songs explore a topic or an issue by looking out at the world, rather than by expressing his or her personal feelings. This is true even when the story or observation contained in the song is told in the first person, very much in the way of good fiction!