Timelines are complicated. So are universes, and so are worlds. These terms are often used interchangeably, but they are each different from one another in very specific, very important ways. A single universe can contain many worlds. A single world must contain many timelines. A single timeline is rife with potential and constantly in flux. Otherwise, free will would mean nothing, and then there would we be?
Well, we would be in most versions of reality, but that's not the point.
Pete's World was an offshoot timeline that refused to fade. Like bacteria, it split off from some original world to grow into a fully-formed place where it slowly shifted out of sync. Rose was never far from a living version of her father. They lived in the same universe.
Ah. Universes.
There are very few universes that have direct parallels—and yet they must, for they are infinite. Worlds within a single universe can grow and split and fade forever; they can breed into smaller dimensions and bleed into a void of infinite dark and appear to be infinite themselves, but they're not. The multiverse can only by inevitable coincidence contain a rare almost-mirror image, and ooh boy are you a rare thing if you ever manage find them, let alone get even from one unrelated universe to another.
This is where our story begins: with a universe in which the Doctor finds something he never does, in one of the worlds where he does the right thing, in the world where she comes back, in the timeline where an impossible gap is bridged, and our universe—not our world in particular, mind you, but our universe—bleeds into another.
She couldn't remember a thing.