Special agent is usually the title for a detective

Detective

A detective is an investigator, either a member of a police agency or a private person. The latter may be known as private investigators or "private eyes"...

 or investigator for a state, county, municipal, federal or tribal government. An agent is a worker for any federal agency, and a secret agent is one who works for an intelligence agency

Intelligence agency

An intelligence agency is a governmental agency that is devoted to information gathering for purposes of national security and defence. Means of information gathering may include espionage, communication interception, cryptanalysis, cooperation with other institutions, and evaluation of public...

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Within the U.S. government, the title of Special Agent is used to describe any federal general or criminal investigator in the GS-1801,1810,1811 or FS-2501

Diplomatic Security Service

The U.S. Diplomatic Security Service is the federal law enforcement arm of the United States Department of State. The majority of its Special Agents are members of the Foreign Service and federal law enforcement agents at the same time, making them unique...

 job series as so titled according to the Office of Personnel Management

Office of Personnel Management

The United States Office of Personnel Management is an independent agency of the United States government that manages the civil service of the federal government. The current Director is John Berry.-History:...

 (OPM) handbook.