In my writings I use certain conventions to highlight particular aspects or qualities of the topics. First, since the language and names are often Chinese in origin, which has multiple systems of transliteration into English spelling, I use Pinyin, the current world standard. This has one major exception that is the name tai chi, which I feel is recognizable now as an English name for this form of practice.
When it comes to the practice of tai chi, the short form referencing taijiquan, I use lower-case. When discussing Tai Chi, the Supreme Ultimate principle, I use initial-cap so that it will stand out.