One way to model the world of public companies is that there is only really one public company, call it The Stock Market Inc., whose shareholders are a bunch of diversified investors. The Stock Market Inc. has a board of directors, made up of the dozen people who run the biggest diversified asset managers, BlackRock Inc. and Vanguard Group and so forth; these people manage money for the people who own most of the shares of The Stock Market Inc. (i.e., most of the shares of each of the underlying actual companies), so they control the votes, so they function like a board of directors.
The Stock Market Inc. does not have a chief executive officer, though; instead it operates through a bunch of autonomous divisions. The divisions are the actual public companies: Apple Inc. is the cool-phone-making division of The Stock Market Inc., GameStop Corp. is the mall-video-game-retailing division of The Stock Market Inc., Timken Co. is the ball-bearings-manufacturing division of The Stock Market Inc., etc. Lots of divisions overlap with other divisions: Delta Air Lines Inc. is the airline division of The Stock Market Inc., and so is United Airlines Holdings Inc., and so is American Airlines Group Inc., etc.