When you write lyrics to deal with emotion or to fulfill a mission, your lyrics are personal. You may not mention yourself at all, but the lyrics are still for or about you (in addition to being for or about others). When you’re telling a story, however, you don’t have to have any personal connection with the plot at all.
Song stories come in many forms. There’s the Couple on the Run from the Law genre (see the incredibly awful “Take the Money and Run,” by Steve Miller Band, and the disturbing, but much better, “Lay Me Down,” by The Dirty Heads, featuring Rome Ramirez). Others are stories about Couples Who Have Depressing and Warped Relationships (see the bizarre “Jack and Diane,” by John Cougar [Mellencamp], and the better but hauntingly depressing “Fast Car,” by Tracy Chapman). Still others are about old(ish) heroes (“Nikola Tesla,” by Joy Electric, or Christopher Lee’s two Charlemagne albums) while others are about contemporary figures (e.g., “Hurricane,” by Bob Dylan, or “Nelson Mandela,” by The Specials).
And then there are the completely fictional story songs, like what I have heard of (or about) Blind Guardian’s and Coheed and Cambria’s work, as well as “2112” by Rush, David Bowie’s The Rise and Fall of Ziggy Stardust and the Spiders from Mars, and Janelle Monáe’s Metropolis albums.
Fictional story songs are much, much older than the “concept albums” of the rock age, of course. They go back to Homer (at least, I hear that what we now read as poems were originally sung) and include the arias from most operas. An important difference here, however, is that the Iliad and Odyssey are about fictional characters, whereas arias in operas are usually songs for fictional characters. We should take a moment to ponder that distinction.