On-site customer is one of the practices of extreme programming, one of the twelve mentioned in the White Book. It says that a customer should sit with the developers in their open work area to be available to answer questions and interact with the development team. Indeed they are part of the development team, and recognize that the success of the team depends as much on them as it does on the developers. They don't have to give up their reqular job to do this, but they must be physically present.
The XP customer is from the business side of the organization not the development side. The customer is someone who will be a beneficiary of the system. They may be a regular user of the system and usually come from the organizations that's paying for the software. Furthermore they are responsible for making decisions about the business value of potential features in the system and describing requirements to the development team. A customer may be one person, but is more commonly a team.