Difference between Private eye and Public eye

private eye—(coll.) a private detective working for a fee:

• The cops don’t like private eyes much.

Cf.: private eyeful —(coll.) a pretty girl or woman employed by a detective agency:

• Both in quality and quantity … this San Francisco private eyeful exceeded her sister sleuths.

public eye—

1. public attention or notice:

• It was a gramophone recording that first brought her before the public eye.

2. public opinion or judgment:

• He resumed his place in the public eye as the thundering Jove of the Opposition.