Even adult dogs grab each other when they're playing, clamping hard and throwing each other around. They have a far different pain threshold than you do.
Puppies do that to YOU because they think you're a dog and part of the pack. Basically they're playing when they grab you with their mouthes, playing as they would with any other dog.
When they're puppies, you have to convince them you're different than a dog.
Its definitely nerve-wracking when your little spawn from hell lunges at your face with teeth bared and snaps its jaws . . . . unless you understand what's behind it.
My two dogs playing, teeth bared.
Cowperson