Even solo modes? Wow. I am still in Evarate or near it, should I move? And how far is "Home territory"? Eravate? I forget.
Yup, even Solo, there is basically one Background Simulation (BGS) that is shared by all modes.
The information is fed between the different platforms (PC, Xbox, PS4), the actual modes themselves (solo, open, private group (PG)) are actually just 'white lists', in solo there is no one on your white list so you never see anyone else, in a PG just the people in the same group are on your list, but in open everyone else in open is on your list and can be seen (subject to instancing).
The Order's home system is Azrael, which is 169ly from Evarate.