If hair and nails are made the same way and both contain keratin, why are they different?

This is due to the fact that nails are not actually some useless piece of accessory on your hands.

Nails actually have several components. The nails actually cover something called the keratogenous Matrix, which is the whitish membrane with nerves, and blood vessels that decide on how far nails grow, and is protected by the nail plate which what you can see. The Lunula or the whitish bit of the nail is actually transparent.

On the other hand you have hair which is a verticle object usually used for aesthetic purposes and is an alive thing until it goes above the skin. Hair which is normally aesthetic does have some purposes in different parts of the body. The eyelashes are designed to keep particulates out of the eye, while the axillary hair, is used for thermoregulation (the hair in the armpits and groin are what makes up the axillary).

As long as it was one lick and the dog is a bigger dog, it should be fine. watch it carefully for a few days.