The break usually happens when you fall and land on your outstretched hands. In fact, the radius is the most commonly broken bone in the arm. Therefore, the medical term for the most common type of 'broken wrist' is a distal radius fracture (that is, the larger forearm bone is broken near the wrist).
The medical term for 'broken bone' is fracture.
The end of the bone nearest the wrist is called the distal end. When someone falls on their outstretched hand, they sometimes get a 'broken wrist.' The bone that is usually broken is called the radius.