Tai.ji.quan versus T'ai.chi.ch'uan

In case you're wondering why there are two different names for Taiji, it goes back to the history of romanizing (using a phonetic notation) for written Chinese.  Because of unique characteristics of the Chinese (Mandarin, to be more accurate), it's practically impossible to transliterate the language into a western language.  Romanization helps us transcribe the sounds, or pronunciations, of characters.

The first widely used romanization of Chinese was developed in 19th centuray through the (independent, but related) works of Thomas Wade and Herbert Giles.  Many reference and well-known books printed in the west about China - before 1979 - used the Wade-Giles notation.  In fact Wade, who was British ambassador in China, published the first Chinese text book in English using this system he devised.  The transcription of the Chinese words for Taiji in Wade-Giles notation is T'ai chi ch'uan.

Later on, during the 60's and 70's, the Chinese government had a new effort in standardizing the romanization of Mandarin for teaching in schools.  The results, officially in place in 1979, is called Pinyin and has replaced the older Wade-Giles system.  It's more flexible in terms of transcribing Chinese sounds.  In this system, the sound that was represented using ch in Wade-Giles is j, and the sound representing ch' is q.  Therefore, in the Pinyin system one  writes Tai ji quan.

Given the fact that Pinyin is the new standard which has practically replaved Wade-Giles, and also listening to how Chinese people actually pronounce the name, I have been consistently using Tai ji Quan or Taiji in short since over the past few years.