Therapists manage mental illness and diagnoses, coaches don't. Coaches work with clients for short periods of time. Therapists can work with clients for extended periods of time. Often, therapists focus on the past and the present, while coaches are focused on the future.
Ultimately, both professions have value and the work can seem quite similar between therapy and training. But once the evaluation, diagnosis, and treatment of mental illness is included, that work becomes therapy. Therapists have rigorous standards of training, supervision and practice, as governed by state or other jurisdictional licensing boards; coaches are accredited by the International Coaching Federation (ICF), which oversees ethics, quality, testing and continuing professional education standards and ensures that coaches have been trained by an accredited training school that requires supervision and mentoring. In addition, due to the legal challenges involved in performing therapies in other states (licensing laws vary from state to state, and many states do not in practice allow telehealth to be provided by therapists licensed in another state), some therapists seek to expand their geographical reach by offering services under a counseling framework.
Because coaching is less regulated, some therapists who are disciplined by state licensing boards choose to pursue coaching instead. Many therapists are diversifying into training services, and many coaches advertise services that look a lot like therapy.