I heard a lot of interesting things two weeks ago at the San Francisco Writers Conference. Among them were discussions of various categories of fiction. Someone asked, "What is the difference between literary fiction and commercial fiction?" The answer came back, "In commercial fiction, you're allowed to have a plot."
John Lescroart gave the keynote address at a luncheon. Annie and I have enjoyed his books for years, and he is one of the best when it comes to legal whodunits. During the Q&A after his talk, one fellow said he was working on a novel, and had thought of it as literary, but noticed it had begun to develop elements of a mystery novel. "So," the fellow asked, "how do I decide which type I am writing?" Lescroart replied, "If a lot of people want to read it, it's a mystery."
On the other hand, in another session, a freelance editor acknowledged that mysteries are more reliable sellers than literary novels, but countered, "No matter how many millions of books Jonathan Franzen sells, he's still going to be considered literary fiction."
Closer to home (my home, that is), there was some puzzling about what distinguishes mystery, suspense and thriller. Laurie R. King spoke in one session about thrillers as books in which the metaphorical ticking clock is in the foreground. I forget where I read it, but I think it is true that suspense differs from mystery in that the protagonist is not a law-enforcement professional (that is, not a police officer, lawyer, private investigator, etc.). This describes most of Hitchcock's films, and most of the writing of Elmore Leonard, Jim Thompson and Cornell Woolrich.
"Suspense" also describes the work of my primary role model, Patricia Highsmith. She is best known for The Talented Mr. Ripley and Strangers on a Train (beware: wikipedia describes them both as "thrillers" though the are not ticking-clock stories). In her book, Plotting and Writing Suspense Fiction, she says a suspense novel is a novel in which there is at least a threat of violence. That would seem to bring us back around to the idea that they are all just novels, and the categories are there to help us find the kind of thing we like.
And, yes, Oedipus the King is best understood as a murder mystery.