In my experience, I’ve seen Presidents working for CEO’s and CEO’s working for Presidents – not to mention combinations of the two. More often, CEO’s work for Presidents.
The President is usually also an officer of the company. The officers and their responsibilities are determined by a corporation’s bylaws.
As far as corporations go: They are owned by shareholders, managed (that is final management authority rests with) by directors and operated by officers and employees.
I don’t think there’s any single standard for the division of duties between “President” and “CEO”. Each company defines it as they wish. Compare it to middle management: Is a “Director” superior to a “Manager”. Maybe so at Exploitco, Inc., but maybe not at Gougem Credit, Ltd.
Now, if it were my company, the head cheese would be the President. The CEO would work for the President and would be the first among equals of the other “chiefs” (i.e. the CFO, COO, CIO, etc.) Either that, or I would abolish all titles except for “Supreme Divine Emperor of Coolness” and “Flunky”.
Plunging like stones from a slingshot on Mars.