In addition to the other comment, company presidents are usually considered lower rank than CEOs, but also often don’t answer directly to them.
A president usually presides over a group, like a board or a council, without direct power over technically lower rank individuals. If a president started micromanaging the cleaning staff, they’d probably be fired.
That being said, company structure varies wildly, and there are definitely company presidents that act more like kings and dictators. It’s just a title after all, no one will arrest you if it’s inaccurate.