So you just thought that a hammer was a hammer.
There are different types of hammers used for different things such as a framing hammer, standard hammer, claw hammer, ball pein hammer, and some are cheap and some are very expensive, such as $300 or above for one hammer.
The part of the Hammer that hits the surface is called the Striking Face. And on some hammers the Striking face can be changed.
Mallets have many uses and are of different design for different tasks. Some for carving, some for hitting wood into place. The standard hammer may have a striking face and a claw for pulling out nails, but the Mallet has two striking faces, front and back.