Yes, the movie producer is like the "boss" of the whole production. He or she is in charge. He gets all the talent together and oversees everything.
Now, in most cases a studio puts up the money for a film. Production companies don't usually have enough money to make movies. Instead, the production company goes to the studio and gets the studio to give them the money - to "green light" the film. So, in a way, the studio executives are the bosses over the producers. If there is a disagreement over how something should be done, the studio executive gets to decide.
When an actor owns his own production company, he usually hires someone to head the company and produce the films. So, let's say George Clooney had his own production company (I don't know, maybe he really does). Let's say he is acting in a movie that his company is producing. That makes him the boss, the "chief of staff" as you say. But if a studio, say Paramount or Universal, is paying to make the film, George has to work with them too. They might give him free reign because he's such a big star, but in the end, they are really the bosses.
I used to work in "the industry."