Popular culture doesn't help either.

US 'police procedural' TV series S.W.A.T.. A heavily-armed paramilitary squad led by a former Marine (of course) and operating from a high-tech base conduct cursory investigations before resolving each case in a hail of gunfire.

UK 'crime drama' series Vera. Fiftyish career copper Detective Chief Inspector Vera Stanhope and her overworked and underpaid but dedicated team, operating from a manky old office, investigate murders with a mixture of diligent enquiries, careful evidence collecting, exhaustive background checks, shrewd questioning and an occasional stroke of luck. You rarely if ever see a gun.

See the difference?