sherlock vs private eye

sherlock and private eye both are nouns.

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

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

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

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

sherlock (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