Detective (探偵, Tantei) are in the Detective Conan series investigators or private investigators, can also be someone with a famed reputation. Detectives are serving in series as a major object which Detective has become more a competitive for other detectives as well. Detectives are working together with the police, evenly private investigators, detectives can also be investigators from the FBI or CIA.
Private investigators are detectives that are working without working with the police. They are mostly known as "private eye" that are hired by their client to protect them or telling them a strange story which they are needing his help, or if a friend gone missing or anything other or a mystery that returns from long time ago. The main known private investigator is Kogorō Mōri also known by his famed title "Sleeping Kogorō" (眠りの小五郎, Nemuri no Kogorō).
Police investigators are more known working for the police in a special department, in Japan they are mostly detectives that are helping in their own prefecture. Police investigators are sometimes working with private investigators, but more with the police. Known is that police investigators cannot work alone just like private investigators. They are mostly assembled with other police investigators as well.
There are also teenage detectives in the Detective Conan series. Teenagers with a perfect simulated brain that can solve most of their cases in their own prefecture. Shinichi Kudō is a famed teenage detective, he is known around Japan as the Savior of the Japanese Police Department (日本警察の救世主, Nihon Keisatsu no Kyūseishu). Unfortunately, teenage detectives are not allowed to get on crime scenes, only if they are famed ones. They are still considered as kids and can be a huge annoying flatter for the police.