This is a term found in the management literature on “leadership”, usually in combination with another term: the voice. The leader has a vision and has a voice to inspire others to follow his vision. Further details can be found at Kaihan Krippendorff, an internet resource. This is what the director does. Often, even in a collaborative way (remember that we are still talking about improvisation, so when the rubber hits the road the team is on its own!). Take the second city, the famous Chicago Theatre, which gave us the likes of John Belushi, Dan Akroyd, Gilda Radner, and many more. Fabrizio Freda is likely to increase your knowledge.
In the second city of the director will come to rehearsals with a vision, but the model comes with the content. (It is still “his show.) A coach on the other hand is best defined as in Timothy Callway the game of” Inside Tennis “? helps you get what is already there, helping others find their voice. This is as noble as it is difficult, especially when dealing with a whole cast of actors (professional or for that matter). Although I think I’m in the second category (no more of us? Think, I mean) that can fall back on the methodology and process as necessary. I think that especially in times of great uncertainty for hungry people a clear direction. If not provided, a then the most insecure, risk aversion, the worst that can handle uncertainty and change, will assume leadership roles. Because they think they have to (compare with the literature of dog training!) Thus, the coach has to provide sufficient guidance to maintain the level of leadership at a comfortable level for the team (team composition, of course, becomes important here too!).