Agency means the girl works for an agency.  You will be talking with the agency, who is the middleman between you and the provider.

Independent means the girl doesn't work for an agency.  You will likely be contacting her directly or, in some cases, an assistant.

Driver means that the girl is independent but that a driver takes her around.  This is of importance if you have a girl coming to a location where it would look weird that a hot girl gets dropped off by a driver.  Typically the driver is also the bodyguard in a sense.  Some drivers come up with the girl (that never works for me), and some are just parked away and available if there are problems.  Girls who have drivers usually call and check in before and after the appointment.  They do the same with agencies.