private eye vs private investigator

private eye and private investigator both are nouns.

Word	Noun	Adjective	Verb	Adverb
private eye	Yes	No	No	No
private investigator	Yes	No	No	No

As nouns, private eye and private investigator are synonyms defined as:

private eye and private investigator: someone who can be employed as a detective to collect information and assist in criminal investigations

Other synonyms of private eye include operative, PI, private detective, shamus, sherlock.

private eye (noun)	private investigator (noun)
someone who can be employed as a detective to collect information and assist in criminal investigations	someone who can be employed as a detective to collect information and assist in criminal investigations