You're correct, it's not different. A lot of those jobs (construction, plumbing / steam-fitting, railworkers, auto plant workers) are unionized too.

Why does the fact that they are unionized matter? The police union is one of the strongest unions in the country and they will even protect obviously bad apples from prosecution. On the one hand, it's good to see unions protect their members, on the other police don't really need more protection from prosecution than they inherently receive just for being officers. It's pretty hard to prosecute an officer even when is obvious to most of society that they've done something wrong that any other person would get some form of punishment for simply because it's in the DA's best interest to not screw with the police, who they require assistance from regularly.