This is by far the simplest world to outline. Essentially, it's just our world, just not quite as we know it. Maybe thirty or forty years have gone by, and the future has come, or maybe thirty years ago things went a little differently (and created a parallel reality). It doesn't matter how it's different so long as it's mostly the same. Heck, it might even be exactly the same, and the characters are just people living their lives (sometimes a little slice-of-life can be nice). I don't know what it might be, but I do know one thing: finding out is gonna be sweet!
P.S. This does mean that things like post-apocalyptic worlds do not fit within this category, as there is nothing but a shared history in common.