A chip shot is meant to be a low trajectory shot with minimal spin. The goal is to get the ball on the green as soon as possible and have the ball roll to the hole like a putt. To hit a chip shot you want to use as little wrists and possible almost like a putt. The club head should never get above your hands.
A pitch shot is meant to be a higher trajectory shot with more spin. The goal is to land the ball closer to the hole and due to the spin and trajectory the ball will stop closer to the original spot at which the ball landed. To hit a pitch shot you now want to use your wrists. The club head should get above your hands now in order to create spin and trajectory.