Have you ever heard John Lee Hooker play jazz? Have you ever heard Howlin Wolf play jazz? Have you ever heard Lightnin Hopkins play jazz? Have you ever heard Elmore James play jazz? Maybe there's more to it than;
but the bedrock blues pattern is One Four Five One. In Jazz, it's Two Five One. If you say it in your Do-Re-Mi's, the Blues chord progression is basically Do-Fa-So-Do. In jazz it's Re-So-Do.
I think it's more to it than that.