The stillness in stillness is not the real stillness.
Only when there is stillness in movement can the spiritual rhythm appear which pervades heaven and earth.
Tai Chi or Taiji?
Both mean the same thing.
The spelling Tai Chi, and its pronunciation "Tie Chee", is from an older translation system called the Wade Giles system.
Taiji (pronounced "Tie Gee") is from the newer translation system, called pinyin, and is closer in sound to the Chinese language.
Remember when we used to say (if you're old enough to remember) Peking? Well, except when ordering duck, we rarely ever hear Peking. That was how we used to pronounce Beijing under the Wade-Giles system.