Private detective
The term private detective is used to refer to those hired to find information about other individuals or organizations. Alternate terms include private investigator or private eye or, simply P.I..
The title "detective" is a rank in many official law enforcement organizations, officials assigned this rank have investigative powers not held by private detectives. They do not have the authority to request search warrants, wiretap warrants, or warrants to read suspect's mail. They can't demand a suspect's identity. They can't compel individuals to answer questions.
Among the jobs private detective take are, surreptitiously following individuals, to report on whether they are cheating on their spouses. If the other spouse is their client, this can help them get better terms in divorce court.
Insurance companies hire private detectives when they suspect an individual has filed a fraudulent insurance claim. If a client claims they require insurance benefits, due to a disabling injury, they may hire private detectives to follow them, and document the client is capable of doing things they claimed their injury prevented them from doing.
When businesses suspect an employee is stealing from them, while they could call on the police to investigate the crime, and on prosecutors to charge them, and try them, they might chose to hire a private detective instead. They might prefer to quietly fire the thief, so their clients don't learn of their vulnerability and lose confidence in them.