This is a bit misleading. Calorie (energy) deficits usually provoke the body into starvation mode, and this can have unwanted effects, including increased fat storage. Some calorie deficient diets are also (accidentally?) low carb diets - the 800 calories/day diet is one. If every one of those calories came from carbohydrate (zero protein, zero fat) you'd only need 200g of carb to produce the 800Kcal. In practice it's more likely that around half the 800 would come from fats and proteins, with the other half coming from 100g carb. 100g carb/day is definitely low carb territory.
The thing about low-carb for me is that it is primarily a way of reducing blood glucose, but it also has the side effect, for me as for many, of triggering fat loss.