The predominant difference between a coach and a therapist is that a therapist works with the past, deep unresolved emotional pain. Traditional psychology is about pathology, or sickness, it works to identify what is wrong or what is broken and helps clients move from a state of dysfunction to functioning. Whereas life coaching is a now and future minded practice which works to identify what is working and what is going right, focusing on specific achievable goals. Coaching is a way of developing a clear and specific desired outcome, and laying out a concise plan of action to successfully reach it.
Therapy is completely appropriate in situations like severe depression, suicidal thoughts, bi-polar disorder etc. Coaching is not a substitute for therapy in these instances, however you can use a coach at the same time; because as a therapist helps you resolve those issues, a coach can help you apply the skills you learn in real life.