The Dynamic wallpaper is the one that moves without using 3D Touch. Those are those little bubbles.
The Live wallpapers only move using 3D Touch. You press down, you see the animation, and the animation goes in reverse as you release your finger. (Cool, but silly.) The live wallpapers move only on the lock screen and it's the fish and the smoke. And again, they DONT MOVE. Only when you press down on it to make it move. ¯\_(ツ)_/¯
The reason why the Live wallpapers aren't the same as the Dynamic wallpapers is because this is consistent with the Live Photos feature that Apple released last year.