The power of a Director is deceptive. Technically, they're the boss. Everyone on a set takes their marching orders from him. If Filmmaking is war, then the Director is the General.
But, like a General, the buck does not stop with the Director. Not only does he have to play nice with high-powered stars, but he has to answer to the Producers, the investors, the studio....
In another type of business, the Director would be upper-middle management. Most of the rank and file falls under him and he manages the project, but ultimately, he has a string of people to answer to. And make happy. And keep happy, if he wants to keep working.