Music THERAPY has to do with contacting, awakening and healing the emotional part of a person. Releasing a traumatic stuck place, expanding self-expression by working through self-intimidation, experiencing inexplicable wordless joy, giving vent to hard sorrows--allowing them to seep out slowly, manageably through the medium of music.
In other words, emotional healing through music therapy takes place not by studying it or understanding it in the cerebellum, but rather by feeling it in the limbic part of the brain. This sort of therapy often defies analysis by the one experiencing it--but it clearly and obviously is FELT. It wonderfully takes place in the non-academic subconscious region of the person's spirit.
Music TRAINING on the other hand has to do with the development of brain function--how it learns to think, progress, organize, distill, decide, memorize and retrieve previous imprinting. Piano practice beautifully strengthens eye-hand coordination, but more importantly, albeit less obviously, further strengthens hemispheric coordination inside the brain itself between its two sides.
It is widely known that IQs are enhanced through systematic, sequential, progressive, consistent, steady musical training. It does for the brain what weight training does for the biceps. It works mental muscle. No doubt about it, it is arduous discipline during its steep initial learning curve--but somewhere along the line it morphs into delightful discipline. Many adults have NOT said, "I wish I hadn't had piano lessons", but rather "Oh, how I wish I had stuck with it longer."
For more, read Renee's e-book on How to Successfully Train Your Children to Master a Musical Instrument.