History of Internal Martial Arts Styles

There's a lot of explanations of what the relationships between the various internal martial arts are, with lots of stories about ancient masters and inclusions of styles so obscure you will never encounter them. I am going to try here to summarize it in a way that only mentions common styles and their relationship to each other. First, understand what Tai Chi is:
http://bfgalbraith.blogspot.com/p/what-is-tai-chi.html

Tai Chi comes from "Wudang Quan," which refers to the old Toaist Martial Arts, just like "Shoulin Kung Fu" refers to old Buddhist martial arts. Wudang Quan is practiced as a style today, and generally looks like a very fast and athletic form of Tai Chi:

Older forms of Wudang Quan also gave birth to the following martial arts styles, starting in the 1600's:

• Chen Tai Chi
• Other old-school Tai Chi like Chen but not Chen, like Wudang Dan Pai, Zhang, etc.
• Hsing-I (a very linear style with a high emphasis on strikes)
• Pa Kua (a very circular style)

In the 1800's Chen Tai Chi was mixed with Hsing-I and Pa Kua and highly standardized by the Yang Family, forming Yang Tai Chi. This became the most popular of all of these arts, and was spread far and wide in China. Yang Tai Chi then in turn gave birth to other styles of Tai Chi:

• "Wu Shu" Tai Chi (has a low emphasis on application and sparring, and a high focus on aesthetics.) This is often called Yang Tai Chi but real Yang Tai Chi has a high focus on application and sparring, and its forms are focused on application rather than on performance aesthetics. Unfortunately this is the most common type of Tai Chi today, and is the style that gives Tai Chi a bad name.
• Chi Kung is exercises originally taught in the Yang Tai Chi, but in Chi Kung no thought is given to application, sparring, or performance, it is only a set of fitness & meditation exercises.
• Sun Tai Chi heavily elaborates on the movement in Yang Tai Chi, expanding it into more of an elaborate kung fu style.
• Wu Tai Chi  emphasizes application and sparring, it is a natural evolution of Yang Tai Chi and is most common style of Tai Chi besides Wu Shu Tai Chi.

All of these above 9 Tai Chi related martial arts are still practiced somewhat commonly today. The Japanese founder of Aikido was a student in China, and had exposure to at least one of these above martial arts there, and Aikido is the Japanese variant of the decedents of Wudang Quan, heavily influenced by various traditional Japanese martial arts.

Yi Quan comes from Hsing-I, and is highly abbreviated and focused on "the basic essentials."

In summary there are two general historical categories of internal martial arts. First are the styles that came before Yang Tai Chi: Chen Tai Chi, other old forms of Tai Chi, Wudang Quan, Hsing-I and Pa Kua. Second is Yang Tai Chi and those that developed at the same time or later, including Wu Tai Chi, Sun Tai Chi, Aikido, and Yi Quan.