"A World of Difference" is the twenty third episode of the Twilight Zone, and was first broadcast in March of 1960. It was written by Richard Matheson, and starred Howard Duff as Arthur Curtis and Eileen Ryan (the mother of Sean Penn) as Nora Reagan.
Arthur Curtis is a normal, 1950s mid-level executive who is working in the office one day when he can't get a signal on the telephone. And then the camera pans and we see that he is on the set of a movie, the telephone is a prop, and the stage crew and director are staring at him angrily because he has blown another scene. They claim that he is an actor named Jerry Reagan who has been given one last chance after problems with alcohol, while he insists that he is Arthur Curtis, suburban modest man. His soon-to-be-ex-wife Nora thinks it is a trick to avoid paying alimony. The episode hinges over whether Arthur Curtis or Jerry Reagan is "real".
This recovers some ground we have seen before, but with a twist: while The Sixteen-Millimeter Shrine glorified a retreat from somber reality to the romanticism of the movies, this show's retreat from "reality" is in the other direction. Beyond the commentary on America's developing relationship with the media and the idealized situations it portrays, this episode also questions the very nature of identity and reality, and the answer given in the episode is up to many interpretations. And as an additional bonus, the fact that the actor is named "Reagan", and that he is a commentary on the blurring between media presentations and real life, is certainly a prescient detail.