How is the story structured in LA Noire?

NO SPOILERS PLEASE

I just bought the complete edition of LA Noire. I am a little confused as to how the games story is structured. I am playing the normal missions in the story mode and I am at a case called the "The Consul's Car"

But if I exit the game and go to the main menu I see there is a cases option in the menu, where I can select my cases. I can obviously play my previous cases but I can also cases a few cases from "Vice" and "Arson", they start out totally random and I can't make out how this fits into the game.

Is the game suppose to work this way?