There are five major styles of t'ai chi ch'uan, each named after the Chinese family from which it originated:
http://en.wikipedia.org/wiki/T'ai_chi_ch'uan
- Chen-style of Chen Wangting (1580–1660)
- Yang-style of Yang Lu-ch'an (1799–1872)
- Wu- or Wu/Hao-style of Wu Yu-hsiang (1812–1880)
- Wu-style of Wu Ch'uan-yu (1834–1902) and his son Wu Chien-ch'uan (1870–1942)
- Sun-style of Sun Lu-t'ang (1861–1932)
http://en.wikipedia.org/wiki/T'ai_chi_ch'uan