The PBX phone system is the traditional analog phone system that has been in use for decades. A PBX system consists of direct line-to-line connections made by an exchange. When your employees pick up a phone and make a call to a customer, they are physically connected through the exchange network.
VoIP systems on the other hand use the Internet to package voice signals into data packets that are transferred over the Internet. So when employees pick up a phone to talk with a customer, the voice signals are transmitted through your network and then over the Internet.