Is there a difference between inherent sugar and added sugar in a product?
Technically yes, since added sugar is usually sucrose and inherent sugar might be fructose, lactose, maltose, etc.
Also knowledge that sugar was added to a product helps you identify sources of possibly unneeded extra sugar.
(This is going to cost multi-millions for food companies to run testing and change their labels)
Presumably they already know how much added sugar their products contain since they put it there. It has been a while since nutritional labels have changed and they could be more informative.
I guess added sugar could also be high fructose corn syrup, which appears to come with some additional problems.