Chi Kung (Qigong) is not a style of Taiji, it's a type of exercise often practiced along with Taiji and other CMAs, which teaches you to control the flow of energy in the body using breath, intent, movement, etc. Someone could have recently coined a new name for their school's Taiji by calling it "Chi Kung Tai Chi," but the major existing schools of Taiji are Chen, Yang, Wu, Hao, Sun and Zhaobao. Whatever this style is, it is almost certainly a variation on one of those.
'Tai Chi Chi Gung' is the name often given to a specific set of eighteen exercises which, although essentially Chi Gung, has moves within it which are used in many Tai Chi Forms. So if there are references to eighteen moves (each move is repeated a few times before moving on to the next), or if it is refered to as 'Shibashi', that's what it is. In my experience it's generally undemanding and has no martial applications, but can be beneficial to health. Of course, it could be something completely different!! Try this link http://taichi18.com/
