Possible Consequences?

When I go into a typical conflict zone, I see system defense vessels and pirate vessels. I know exactly who to shoot at. So last night I'm working my way up the Federation ranks, and I'm in a Federation system, and I want to try out some new weapons, so I head over to a local conflict zone. I see Federation Navy Team A (actually "blue" something or other) fighting Federation Navy Team B (actually "values" something or other). Both show as neutral for me. All the ships say "Federal Navy" when I target them. I had to just leave, because I can't see myself shooting Federal Navy ships, and I couldn't fathom why two groups in the same navy were firing on each other.

So I was wondering, from a game perspective, how does this work? Do I gain or lose Federation points if I fire on one or the other? Are these even meaningful alliances? Should I pick a side, or just stay out of it? What are the consequences, if any? TBH, I'll probably just go elsewhere and find some pirates to pick on, but it would be helpful to udnerstand how this works.