That's just the way the moons look in the Elder Scrolls. The setting of the Elder Scrolls is not Earth and has its own moons that are quite different from our own moon. There's some lore on the moons but the lore forum would be a more fitting place to go into detail on that. As to what you see in the game, as you can see, there are two distinct moons that follow their own cycle in the sky, much as the moon does in real life, you can also see that they take up a lot more of the visible sky than our own moon tends to.
I've never noticed the surface of the moons moving, though.