There are overlaps and similarities in methods, and all disciplines are evolving, however they are not the same thing. There is an important difference in the two approaches.
Therapy, along with psychology, psychotherapy etc., is related to Human Sciences; they look at the human being from an objective standpoint, as experts. The attention is more often on what is going wrong, and understanding why. The interaction follows a plan that comes from the specialist's knowledge and experience, in response to a diagnostic s/he makes.
The focus is on problems, mostly looking at the present and into the past.
Coaching is looking at the human being as a person, a naturally creative, resourceful and whole person and therefore endlessly surprising and totally unique. The focus is on your strengths and how you can build on them to overcome obstacles, whether internal or external. There is nothing broken in you. We are looking at what you achieved, what qualities in you made these achievements possible and who you are becoming in the process. It is about looking at you in your "fullness" and evoking your transformation.
So for example we will look at emotions as being part of you, they are not something to suppress, dangerous or scary. By giving the time and the space to fully experience emotions, coaching will support you in moving forward, stronger from having learnt from them. The focus is on solutions, and it is about you finding them, and finding them your way. Starting from the present and moving into the future.
And it could happen that something needs more attention, something that keeps you stuck, or you need specific advice. In this case I would refer you to other professionals. Sometimes it is even possible to have coaching at the same time as therapy or mentoring etc. There is a detailed code of conduct that I follow as a professional coach that provides a guideline on when it is advisable to refer clients to therapy.