Rod puppets are built on dowels (the puppet's spine) with rods to manipulate the arms. Rods are usually attached to wrists and feet (perhaps ankles, if the puppet needs to dance). They can be built around a dowel (approximately the width of a broomstick so they're easy to grasp for long periods of time), or be a hand puppet that uses rods to manipulate the arms, called a hand-in-rod. Rod puppets are very old; examples of ivory rod puppets have been found in Egyptian tombs. Kermit the Frog is a rod puppet because rods move his arms. The photo is of a dancer rod puppet from Bengal.
Shadow puppets continue to be popular in the Mid- and Far-East. Some cultures don't allow live performances of plays, so shadow puppets fill that dramatic gap. Shadow puppets in China go back two millenia, where they played to all social classes, not just the nobility. The ones cited are from Bali; similar shadow puppets, called "wayang kulit," are from Java (see photo). Shadow puppets also traveled to the west to Turkey, where they're called Karagoz.