If you get into mysteries very much, you'll discover there are some basic differences between cop shows and detective shows. The key is the nature of the authority.
Cop shows themselves are fairly easily divisible into procedurals, character-driven workplace ensembles and social dramas. One type found in literary mysteries, the humdrum, does seem pretty much missing from the screen.
Detective shows are also divisible into great eccentrics, madcaps, cozies and hardboiled.
Then there is the closely related crime show, which is fairly easily divisible into social realist and hysterical reactionary. Oops, almost forgot the caper.
Whoever thinks all cop shows are the same just doesn't understand what they're seeing on screen.