Here's a wonderful description of one directing style - Robert Altman as described by Graeme Clifford and Mark Rydell. Bob Fosse had an extremely different approach. They were both looking for the best from people. I think these styles are not mutually exclusive and can actually be used together. I find myself borrowing a little from each when I direct.

Friday, March 12, 2010
delanceyplace.com 3/12/10 - styles of directing

In today's excerpt - successful movie directors can be found within every style and personality type, from highly controlled and controlling to flexible and improvisational. Robert Altman (M*A*S*H, Nashville, McCabe and Mrs. Miller, The Player) was an extreme example of the improvisational approach:
"GRAEME CLIFFORD (assistant director): Altman had a preproduction speech at the beginning of [a] movie that just captured his whole approach. He said, 'Anybody can come up to me at any time and give me any ideas they have or discuss anything they want. Sometimes I'll use them and sometimes I won't. I may not always have time to tell you why I'm not going to use your idea, but I'll always listen.' I didn't work for anybody else for the next five years, and I just assumed everybody worked this way - the way he treated the crew, the way he treated actors. I stole that speech and I use it on any movie I make, but you think many directors say that? ...
"MARK RYDELL (actor and director): Bob [Altman] sent me the script [to The Long Goodbye]. I looked at it and thought, 'This part is just not well written.' So I called him and I said, 'Bob, what would you think if I rewrote this part and made it two hundred percent better? I have a concept for a character.' He said, 'Go ahead.' The character in the book was wishy-washy, really, had no character. ... So Larry Tucker and I decided to make him this Jewish gangster who was insanely brutal, completely capable of any kind of brutality, yet at the same time deeply religious, offended that he wasn't in shul, where he should have been on this night. At the same time, the challenge was to make it funny. Make it not only cruel and horrendous, but charming and funny. So we did that. And we sent the pages to Bob. He called back in five minutes and said, 'That's it. Throw out everything else, I'm inserting your pages right in the script.' That's the kind of guy he was. All he wanted was the best from his people.
"One of the first things he used to say on a set was, 'I'm interested in everything you have to bring.' So he had that remarkably paternal and constructive quality of nurturing people and giving them permission to be as good as they can be. He rarely directed them in obvious ways. His ways were more subtle. He would encourage you. 'What've you got in mind?' he would say. 'Show me. That's great, let's use it.'
"His directorial style was improvisational and permissive. And actors loved him because of it. Because they could bring their skills and their instincts, which he admired and respected, to the moment. If it came from you, he was interested. He didn't want to give you something and have you execute it because he knew that anything he gives you is by nature less good than what you come up with yourself. He instinctively knew that the way to get relaxed and realistic performances was to encourage the creative spirit of each individual actor, and he cast that way. He cast in an effort to find people who are inventive."

Mitchell Zuckoff, Robert Altman, Knopf, Copyright 2009 by the Estate of Robert B.
Altman and Mitchell Zuckoff, pp. 155, 248.