Mouthing is a normal dog behavior. Mouthing is more of open mouth lots of tongue slurring around the object. It's a form of play, but should not be allowed.
Nipping is the teeth grazing and can even tug but never actually harms or breaks skin.
Actual Biting means the dog is using most if not ALL of its jaw power to put down pressure. You would at this moment definitely respond quickly as this would cause pain.
Why dogs bite? It has nothing to do with being mean . More often than not a dog bites out of fear rather than aggression. Dogs are territorial creatures and will protect their area . If you are threatened by an aggressive dog:
Remain calm. DONT Run .You wont win. never turn your back. walk backwards slowly.
Avoid eye Contact ,Do not smile at the dog, use soft soothing voice loud angry sounds make the dog more aggressive. And Don't hit the dog, it makes the situation worse.