Players can be improved/upgraded. The game will add a new player  you just received who has a potential to be a higher rating to the active if you choose the "potential" option.

So for example, if one were to draw a player who can be upgraded all the way to a Gold rating, he has more potential than another player who can only be upgraded to the silver rating.

If "current" option is chosen it only looks at the current rating, and not what it could potentially be once upgraded.