Don't think there's a difference between single and multi, and that said you have it right. I'd also go so far to add the bottom portion-- the omega systems-- as a fifth and hardest area. Don't recall them being claimed by one of the others.

Aye the omega systems are insane, not only are you fighting against nothing but sabers and titans but you also have to navigate some nasty space with neutron stars that literally eat away at your hull if you get close, lots of radiation, lots of gas clouds, asteroids, etc, etc....very tough places to be, especially if you're not friendly with the corsairs, red hassains and the outcasts.