Actually, each branch operates the same way; receive orders on target, capture them, perform an Erasure. The reason there are multiple branches is because Chicago is now so massive that it requires it. One single branch can't handle the entire city. 

We'll be delving into the specifics of Erasure itself when we get to the first target. Then you'll understand how your characters can specialize in certain tactics and what have you because if I explain it here, it will be a LOT of exposition.