Technically speaking, there is a difference between relaxation massage and therapeutic massage. Oftentimes, relaxation is half the battle, so relaxation massage could also be defined as therapeutic. Relaxation massage is meant to relax you which could be a therapeutic goal.
Therapeutic massage is also meant to relax you, but typically there is a more specific goal in mind. If you have a specific health condition, for example, a massage therapist will aim to assess and treat your condition, whereas a relaxation massage practitioner will aim to help you relax.
If you train in therapeutic massage, you will learn how to manage and treat specific health conditions. There are so many different types of massage modalities, and so many different types of massage training, and they are all therapeutic, but in the technical sense, there is a big difference not only in the number of hours of training but in the training itself. See Massage Training for more information.