The way I read that as a diabetic is Sugar Free is free of refined sugars and has a carb leval less then 13 (equal to the number for 1 diabetic food exchange. "No Added Sugar" Means that the food its self (such as an apple in the apple pie) contains sugar (in its natural form) and that they have added no refined sugars to the food item.
This is how my doctor told me to decode that myth. But it could be different for just watching carbs. Be careful because sugar free is not all ways carb free. Check those lables.