Director v. Coach
It took me a really long time to see a distinction between coaching and directing for improv. They were more or less the same thing for me. When I finally did draw a line it helped me work with teams a lot more effectively.
Coaching is working with a group to improve their performance around goals.
Directing is working with a group to help them achieve the best they can with a form or show.
You can coach when you're directing, but I hesitate to direct when I coach.
Setting these definitions for teams you work with will make the expectations of the sessions clear.
If you're a coach it's common to be asked for assistance with developing a form. And when directing you'll need to work on specific skills and performance styles. So why is this distinction helpful?
I use this to plan rehearsal sessions and get people in the best headspace to work. In planning a coaching session I talk with the players and prioritize some elements of play that might help with their form but it is not specifically tied to elements of it. The sessions are flexible with types of games and exercises and have more individual guidance.
In a directorial session, I plan to work closely with the devices and stagecraft of the form. This looks like more full runs, more repetition of form elements (eg openings), group feedback.
Keeping this in mind helps me not spend a session bopping back and forth from these and make the best use of our time.