Taijiquan vs. Western Tai Chi?

The five traditional schools of Chen style, Yang Style, Wu Style, Hao style and Sun style Tai Chi are martial arts styles with combat applications. The Tai Chi mostly taught in the west as an exercise form is merely a watered down version stripped of the combat applications. If you are interested in learning a martial art along with health benefits, then try to find a qualified instructor in one of the five styles listed above. If you're just after the health benefits, then any Tai Chi cl with a qualified instructor will do. Just remember, the traditional styles are very different from the simplified version taught in the west, they contain longer forms than the exercise version.