Simple ≠ easy

The equation is simple. Actually losing weight is difficult. This is what confused me about your first comment, I couldn't tell if you were saying that it was not simple or not easy. And as you said, losing weight could be lost as either fat or muscle. If your energy intake is less than what you need to sustain your body, the body will take from your reserves (could be fat or muscles).

I am sure there are complexites to this that I am missing, like what happens if you were to starve then start eating again. The advise I find to be the best is to try to find a diet that you can maintain indefinitely. That does not mean to never eat ice cream, it means to eat less ice cream. If you are eating one bag of chips per day, make it once a weak. Did you eat X today, don't eat Y as well

Gaining muscles though, all I know about that is mostly nothing so I won't speak on it.