I don’t really know what the function of mop-up is in the fatigue drop down. If using minutes, it makes more sense, but on the fatigue side, all the other options (besides rest) indicate when the player is pulled, not when he’s used. As far as I’ve ever been able to tell, if a player is off the depth chart, he does not play in games. It doesn’t matter where his fatigue setting (or minutes setting) is fixed.
You may be right, maybe the difference is that with rest, an injured player remains where they are on the depth chart, but doesn’t play, whereas with mop-up, they may come in, but only under certain conditions. I certainly don’t use it, maybe others know more about it.