I see it that way too. I would think it's like combat today, where your destroyer or base of operations would get orders from a higher command. You as a pilot speak directly to your base of operations command officer during a mission, where they have the perogative (based on parameters set by a higher command) on how many ships can be used for the mission, mission design, reinforcements, etc and still be able to operate in the theater of combat. Your command ship in turn reports to their high command when they need to be authorized for a change in objectives.
For instance, the high command orders your command ship/destroyer to disable a new weapons facility. Your command ship would have capable officers to create the mission from start to finish based on high commands objectives, how much force would be needed and how many ships would be needed to disable that facility and still be a viable resource to that theater.
If, during that mission, one of the pilots discovers a transport leaving the facility, your command ship has the personal capacity to modify the objectives without high commands involvement to include disabling, scanning, or destroying that transport. But if there is a particular circumstance that would drastically change the outcome of the mission or the war itself, your command ship would have to notify the high command for further orders during that mission.
On how your command actually sees: I think it's like what others have said already. They see a 3d representation of the theater, using information sent from the sensors on every ship in that theater (whether it be capital, fighter, probe, beacon, turret, etc) in real-time.
High command (based in some command installation away from the theater of war so as to not get destroyed) wouldn't know exactly what each theater had going on in real-time. They'd have a larger "map" of space showing where the particular engagements and positions were and update it periodically by their communications officers coordinating with your command ship.
Anyway, I could just be talking fluff.