story that is based on a song, and incorporates lyrics from said song
I read a Murder By Numbers songfic last night based on a John Mayer song.
An often exceedingly craptastic piece of fanfiction which alternates between a story and song lyrics. Not a bad idea by itself, but usually not done very well at all.
I read a songfic last night to 'Sk8er Boi'. I wish to hunt down and torture the author.
A fan fiction based around or inspired by a song. Similar to a music video in the sense that it has a story that complements the song.
That songfic really went along that song well.