The underlying principle is that you can only take in as much air as there is available space in your lungs. So if there is still air in your lungs when you try to breathe in, the amount of air you're going to be able to take in will be limited. And the air that is still remaining in your lungs will be carbon dioxide. So you will feel the need to breathe again sooner than if you had exhaled all of the air from your lungs before taking a breath.
Another reason for using the first method is because blowing out air through your nose just as your nose and mouth are surfacing will reduce the chances that you will inhale water (which can be very uncomfortable).