Coaching is so complex and yet so simple that describing how it works is all but impossible to do. A coach guides you through your own assessment, helps you identify your own best solution, and stays with you as you implement your own strategies. A mentor has become successful in the line of work you have chosen. Mentors typically do not charge for their services. In addition to an excellent understanding of human nature, a professional coach has been trained to coach many different types of personalities engaged in an infinite variety of endeavors, both in their careers and in their personal lives.
Coaches charge for their services.
You get the idea. Counseling or psychotherapy is about resolving the past, where as coaching is looking forward at opportunities and the possibilities in one's future. There is very little difference in coaching specialties. Coaches are always coming up with new ways to set themselves apart - creativity coach, strategy coach, life coach, spiritual coach, etc. It's just a way to let people know they are interested in a particular kind of situation, but good coaching is still always directed to who you are, not your line of work or a given situation.