AirlineFlightSchedule has information on the upcoming schedules for an airline. The distinction between AirlineFlightSchedules and Scheduled is that AirlineFlightSchedules will return results related just to airlines (and the return data is more specific to the aircraft that airlines fly) while Scheduled will show any flights (both airlines and GA) that have filed an IFR clearance for a given airport. To create your timetables you’ll most likely have to use a combination of at least the Enroute and Scheduled (and AirlineFlightSchedule if you want additional info on airline flights) methods. If you want information on recently arrived flights then you can also use the Arrived method and for information on which planes just left an airport you can use Departed.
For in-flight aircraft positions you use the SearchBirdseyeInFlight method to get updates. Depending on which aircraft you want position information on will determine what query parameters you need to pass into the method.
Hopefully that helps clear up some of your confusion.