Yes and no! Both are caused by Insulin lacking, however of the two types, little Insulin (type 1-dm), or relatively too little (type 2-dm) caused by the body becoming resistant to it's own insulin. Insulin is necessary to put fat in a cell, without it you burn fat, as in juvenile onset type-1 dm. Most people do not know that type-2 dm is far more hereditable than type one.
Carbs, I believe you are refer to Insulin resistance. This is usually inherited disorder in which your body's Insulin is not carrying the breakdown of "carbs" --glucose into the body cells efficiently. So, your body cells (muscle, brain) want to get supplied the glucose ..But it doesn't happen. The glucose that is misdirected is made into triglycerides and very soon more body fat! more hunger! more.