Medical massage is generally used to identify clinical massage performed under a physician's prescription. This is usually accompanied by the need to bill an insurance company for the services, communication with the insurance company, primary care physician, physical therapist, other practitioners, and attorneys.
A medical massage, inside the treatment room, will look very much like the previous description of clinical massage.
Medical massage and clinical massage are separate services.
Medical massage includes clinical massage, but also includes other services, such as handling the billing process, dealing with insurance companies, producing comprehensive visit notes and narrative assessments as necessary, etc., and requires time and expertise outside the treatment room.
A more complete description of the difference between clinical massage and medical massage can be found here.