This definition is entirely dependent on the internal mind state of the individual. The guy behind the counter of the local 7-Eleven may think he's smarter than everyone, and may think he should be in charge, but nobody thinks of him as an elite.
I'd guess most people today consider an elite as somebody who wields influence within a political, corporate, or other type of entity that itself is highly influential within society, and who is well connected to other people of influence.