private detective vs private eye

private detective and private eye both are nouns.

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

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

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

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

private detective (noun)	private eye (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