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My teachers believe that the creative producer's job is to service the vision of the director, to stay within schedule and budget, and to get the studio what they need, but you work for the director to get their vision on the screen. That's not how everyone approaches producing, but it is certainly how directors like you to approach producing. How I was brought up is that my job is to help you make the movie you want to make.

Source: collider.com
My teachers believe that the creative producer's job is to service the vision of the director, to stay within schedule and budget, and to get the studio what they need, but you work for the director to get their vision