Yes, I think there's a difference between the two also. But whether you're an instructor or a coach or both, you have to be able to read the player you're trying to help.I think you hit on the difference between an instructor and a coach.
The way I see it, an instructor is for beginners and intermediate players. Players who never had a proper stance or cue delivery.
A coach is for higher level and pro players, who don't need the changing of fundamentals. Maybe a polish.
In every sport there are instructors who teach at high levels. So why would you limit them in pool to just beginners and intermediates?