I think the difference is perception, Lisa.
Any decent personal trainer needs to see the tie between what the mind thinks and the body does. Personally, my technique i have been developing over the past eight years takes the mind out of the equation and allows the body to do things that the client’s mind had deemed impossible (ie and older man being told he can’t walk by “experts” and his mind making that a reality physically).
The difference is usually the arena. The transcendental, peaceful worlds of tai chi, quigong, or yoga are seen as mind-body activities, where as muscle development somehow gets classified into the hardcore, dumb muscle area. I like to blend them. Both are important for both mind and body.