A Mutex controls access to a single shared resource. It provides operations to acquire() access to that resource and release() it when done.
A Semaphore controls access to a shared pool of resources. It provides operations to Wait() until one of the resources in the pool becomes available, and Signal() when it is given back to the pool.
When number of resources a Semaphore protects is greater than 1, it is called a Counting Semaphore. When it controls one resource, it is called a Boolean Semaphore. A boolean semaphore is equivalent to a mutex.
Thus a Semaphore is a higher level abstraction than Mutex. A Mutex can be implemented using a Semaphore but not the other way around.