Coaching always looks forward, to the future, to getting what the client wants.
Therapy and counseling frequently look backward, to what went wrong in the past, to analysis.
In coaching, I believe my clients are whole, absolutely all right, and already has all the resources they need to succeed. My job is to help them unlock their genius. It's not about "fixing" problems, or blaming and shaming, it's about moving forward to meet goals. A client in crisis (say, any kind of mental health issues or some other trauma) may not benefit from coaching. I am the first to say that I cannot help someone in crisis, and I do refer them to other professionals, as appropriate.
Counseling and therapy tend to look more at what is not whole, what might be broken, or what is in crisis. This is important, and it's complementary to coaching for some clients. Coaching is a powerful method for getting what you want, but it is no replacement for therapy or counseling when these are needed.