The difference between low-carb and no-flour-no-sugar?
 

It seems that the no-flour-no-sugar diet is basically a low-carb diet where you're allowed fruits and vegetables? Is there something more to it than this? If the whole principle of low-carb/Atkins was that you were burning off fat because of staying away from carbs, then how is one losing on the NFNS diet while eating foods fairly high in carbs like some fruits and veges?

Big difference in processed carbs (flour and sugar) vs natural carbs (fruit and veg).