Slaughterhouse Five: Connection Between Kurt Vonnegut and Billy Pilgrim

"Billy answered. There was a drunk on the other end. Billy could almost smell his breath—mustard gas and roses. It was a wrong number. Billy hung up." Kurt Vonnegut Pg. 73

I've heard a lot of theories about just how Kurt Vonnegut as a narrator and Billy Pilgrim connect. Some people think that Billy and Kurt know each other somehow and he's telling Billy's story that Billy told him. Other people think that Billy is famous for being the crazy nut and that Kurt just wrote down the stories he heard. Then other people suggest a much more far out theory. Some people think that Billy Pilgrim and Kurt Vonnegut are actually the same person. I highly doubt that though because there are certain times in the book where Kurt will mention that he was at the same place where Billy was. They can't really be at the same place doing different things if they are the same person. Even if they aren't the same person they must be connected somehow, but how? Why does Vonnegut feel the need to tell Billy's story? Clearly it's important to him but why? Hopefully it will be revealed later in the book, but I know I can at least rule out that they are the same person.