limelight vs public eye

limelight and public eye both are nouns.

Word	Noun	Adjective	Verb	Adverb
limelight	Yes	No	No	No
public eye	Yes	No	No	No

As nouns, limelight and public eye are synonyms defined as:

Other synonyms of limelight include glare, spotlight.

limelight (noun)	public eye (noun)
a lamp consisting of a flame directed at a cylinder of lime with a lens to concentrate the light; formerly used for stage lighting	a focus of public attention
a focus of public attention