Your score and moves depend on where you are in the current game, which is the one you've restored. Awards are awarded to you for something you've done, and are not restricted to a single game, there are many awards for the different ways you can be killed in the game and making awards persistent means you can collect more than one of these. If you restore a game where you're close to the end, you may get the points, but you won't pick up all of the awards you would have got along the way.