Where Tai Chi consists of a series of movements linked together in a form, Qigong usually consists of much shorter sets of movements linked together, with a primary focus on building the internal energy pathways in the body.
Qigong is more strongly associated with the Eastern medicine five organ systems, which is a whole other discussion best presented in a class. As an overview, the energy meridians in the body (the ones used by acupuncturists) are all linked with an organ system. Those organ systems have strengths and weaknesses, positive/negative emotions and are assigned a season, among other things.
In Eastern medicine, specific Qigong exercises might be prescribed to assist with an ailment that a doctor identifies as associated with an out of balance issue with a particular organ system. I am not an Eastern medicine doctor and cannot diagnose illnesses, however, it is necessary to understand the basics to truly work with Qigong.
Qigong also consists of meditations that train the mind to move the energy throughout the body. Taoist Qigong, uses concepts that are more esoteric, such as alchemy transformations of the life force. Again, this is a series of studies best presented in classes.
In general, using gentle stretching exercises combined with breathing techniques, Qigong aims to balance the energy throughout the body, promote health, as well as strengthen the body, mind and spirit. While the exercises are simple and can be easily performed by most reasonably healthy individuals, the practices do build physical, as well as energetic, strength in the body.