The terms Private Eye, Private Detective, or Private Investigator are often used interchangeably. A private investigator (often abbreviated to PI and informally called a private eye), a private detective, or inquiry agent, is a person who can be hired by individuals or groups to undertake investigatory law services.
According to PI Magazine, an industry trade publication, historically the profession of non-law enforcement investigations started back with Pinkerton in the late 1800s, but beginning around 1960 many states did not want the public to confuse a private detective with that of a police detective so we adopted the term Private Investigator.
A detective is usually a police officer. A private investigator does not have the authority of police power and operates under the powers of an ordinary citizen. This means that, for example, they do not have the authority to compel entry into real property, or the authority to make arrests (outside the citizen’s arrest doctrine.) Many people still call Private Investigators Detectives or Private Detectives.
Most Private investigators work civil cases or work criminal defense (which means gathering evidence on witnesses in a criminal trial). Their objectives they seek are also quite different if you are referring to police detectives. They are members of a police department or law enforcement agency.
The term private eye has widespread use to mean private detective or investigator. Several websites suggest that the term was based on a logo adopted by the Pinkerton agency which featured an eye and the words We Never Sleep. However, none of those sources seem authoritative or provide any reference to a contemporaneous usage of the term. Pinkerton registered the trademark "We Never Sleep" with an eye logo in 1950, claiming that it first used the trademark in 1884. Numerous websites (again lacking authority) and at least one dictionary cite the derivation as "1935–40; eye, allusive phonetic rendering of [the letter] I, abbr. of investigator". Therefore Private Eye (I) would literally mean Private Investigator.