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Tai Chi includes many practices
"The Form" = T'ai Chi Ch'uan / Taijiquan = a solo practice
The style we teach in TCF is the 37-posture Yang Short Form, as developed by Professor Cheng Man-Ch'ing - the first person to teach his Tai Chi outside of China. There are other Yang styles, and other styles whose lineage is via other ancient families, eg Chen or Wu. China once banned Tai Chi, but has now re-introduced a 24-posture "official" form.
"Sensing Hands" = Twey Shou / Tui Shou = a 2 person practice
This is a Tai Chi partner exercise that challenges students to continue to embody Tai Chi principles whilst interacting with another person - an additional distraction / pressure. Contact with a partner gives immediate feedback on your internal state. They are trying to sense, and then use, any tension (lack of relaxation) in you. You are trying to sense, and use, any tension in them. Both of you are learning to relax into all types of interaction.
We teach Sensing Hands (or Push Hands) to those who have done Fundamentals form.
3 minutes on the concept of Qi
"Sword" = T'ai Chi Chien / Taiji Jian = both a solo practice ("Sword form") and a 2 person practice ("Fencing")
Sword form and fencing are taught only to experienced students - typically on TCF trainings or special weekend workshops.
"Roots & Branches" (5 Element Qigong) = Ch'i Kung / Qigong = a wellbeing practice
"All Tai Chi is Qigong, but not all Qigong is Tai Chi." Ours definitely is, as it works with the flow of energy inherent in our form movements and focuses us on how they develop our Qi (or Ch'i), the Chinese word for energy - what, in this context, we might call "life force". Qigong uses mental imagery and a focus on breathing, combined with either holding of an individual position, or continuously moving between left and right versions of the position - sometimes developing this into a flowing "walk".
When we run Qigong workshops, we typically focus on the one particular type of energy associated with the season, which is also represented by a particular "element". In the Chinese system there are 5 seasons and 5 associated elements:
Winter / Water
Spring / Wood
Summer / Fire
Late Summer / Earth
Autumn / Metal
Although Qi is pronounced a bit like the Chi in Tai Chi, it is a different Chinese word. The video from TCF's "Roots & Branches" DVD explains the concept of "Qi".