when you're in a fasted state, your body goes through hormonal changes. think of it like your body going into survival mode because it doesn't know when you're going to eat next. think back to the hunter/gatherer days, hunters probably went days without eating but they still needed the energy to do so. so, in a fasted state, their bodies switched to using fat as energy, increased their metabolism, increased their hgh, energy levels, and mental clarity so they would be ready. While most of us don't hunt for food anymore, our body goes through the same changes.
when you severely restrict calories, your body doesn't go through those hormonal changes because you're still taking in food. however, because you're taking in a lot less than what your body needs, your body will make changes to adjust. these changes can included reduced metabolism and, in cases of extreme caloric deficits, pulling nutrients out of areas it doesn't think is necessary for survival such as nails and hair follicles, which is why hair loss is common. other changes you might experience is drop in body temperature because it takes energy to keep you warm and, since you aren't getting in enough calories for other needs, it drops your core temperature. also, while some fat is used for energy, your body will start burning more muscle for fuel because your fat is going to be a primary fuel source if comes to that. it basically saying 'i'm not getting enough calories, lets save as much fat as we can just in case.'.
on days that you do eat, eating as close to your bmr or having a much smaller deficit will keep your metabolism burning near optimum for weight loss. you're metabolism will always drop with any kind of deficit, but a slow and steady drop is much easier to control than a sudden drop. and, i don't know for sure but i think, while in a fasted state, your body will adjust to your changes in metabolism. so, if you keep your caloric intake high to burn as many calories possible, your body will do burn fat a lot more effectively while in a fasted state. remember being in a full fasted state ramps up metabolism. at the same time, if you're at a severe caloric deficit and only, say, eating 60% of your require calories, then your metabolism will adjust and won't be as affective while in a fully fasted state. i could be wrong, though. but i found i have much better results during an extended fast when i've been eating a lot more calories.