"A mutex is really a semaphore with value 1"While mutexes indeed are similar to binary semaphores, there is one significant difference: the principle of ownership. And fortunately Niall picked up that up in his excellent series on Mutexes vs. Semaphores. Here is part 1, part 2 and part 3.
No, no and no again. Unfortunately this kind of talk leads to all sorts of confusion and misunderstanding
Another one, more compact explanation comes from Michael Barr in Mutexes and Semaphores Demystified.