What are the differences between PC and professional simulators?
The main difference is in the flight dynamics model. A PC simulator can be realistic, but who is to say that it is? A professional simulator must show to the authorities (EASA,FAA etc) that the modelled behaviour matches flight data.

There are several authorisation levels, from very basic to zero-flight-time. Even for the basic devices, the authorities want to make sure that only correct cues are generated and that there never will be any negative training habits formed by the simulator user.

PC-based programs can teach students where the buttons and indicators are, what to push, which instrument to monitor far what etc. Some of them are accredited by the authorities, more info in answers to this question.