I've worked with some psychologists giving business consulting, and they would use the definition from the International Coaching Federation (ICF), which is that coaching is "partnering with clients in a thought-provoking and creative process that inspires them to maximize their personal and professional potential".

So in that sense a coach would not set the agenda at all, nor be directive of what you need to do to get there, quite the opposite in fact. They keep asking questions and pushing you to figure out what you need to do to get there, which means that a coach can theoritically help you even if not in the same field as you.