This is my take on it, and please correct me. These are all policing titles (official) I can think of: Authority, Police Officer, Sheriff, Deputy, Patrol. And then coming to mind are just the "security" so they're uniformed but not certified as officers at all, armed or not, they might be able to detain until an officer can arrive and make an arrest(?).

Then the "districting" that comes to mind would be funky down at the rural level because villages and unincorporated communities need to share jurisdiction with a "greater" township, so - I am gonna call them all "Communities" as small areas for policing with headquarters being shared by community and then level up to county, county seat and courthouse, etc. Larger communities I guess I have to call municipalities - these are so large they're broken (well, historic boundaries are maintained) into smaller districts within, for example, Greater Milwaukee, not to say it's the same as a city's weather radar area but certainly . . . Downtown is surrounded by "precincts" with stations and headquarters answering to a central municipal body. I dunno. I kinda know what I'm trying to say. feel free to be nice and fix what I tied to lay out, pleassse