Just wondering if someone could dumb down for me the explanation of whether the operation is private, charter or RPT... Especially the difference between a charter and it being RPT....

You are correct in noting that the main difference between RPT and CHTR is that RPT operators can publish a timetable and fly fixed schedules along fixed routes with seats available to the general public.  A CHTR operator can charge for seats on a flight but cannot fly a fixed schedule along fixed routes.

One way to look at is to consider the difference between a bus and a taxi.  A bus can operate to a time table along fixed routes, but at taxi can only respond to demand.  The passengers approach the taxi driver and request that he takes them to a fixed address.  But the taxi operator cannot advertise that he leaves a certain location every day at a fixed time for a fixed destination.  He/She can only respond to demand.