FWIW, very simply put,
NO, sugarfree is not carbohydrate free.
Carbohydrates (C-H-O) contain carbon, hydrogen and oxygen molecules.
Sugar(s) is/are one type of carbohyrate.
Carbs are essntial for proper nutrition and brain function. They are not evil!
I eat very little, if any, sugar, and quite a few "carbs" each and every day.
Hope this helps.
Mark