Danjo said:
This may be ignorant, but I read somewhere that "internal" referred to taoist arts created within China and the "external" referred to Buddhist arts brought to China from India. Has anyone else heard of this definition, or was the source a crackpot?
The long answer
The source is not a crackpot, but not entirely correct either. And if they are from Taoist or Buddhist sources they tend to be the philosophical side not the religious. Also there are some that are Muslim.
Internal styles
Tai Chi if you agree with the most excepted history comes from a Taoist named Chang, Sen-Feng. However the Chen family claims it is exclusively from them. Either way it has a basis in the Tao Te ching with is decidedly Taoist.
Xingyiquans origins are not as certain but it is usually credited to General Yue Fei of the Song Dynasty. He created it (at least the 5 element form) for his officers or soldiers for combat; I do not believe neither Taoism nor Buddhism is associated with General Yue Fei, as far as Xingyi goes.
There is also some argument that Xingyiquan at least the animal styles are from the Shaolin temple, if true this is Buddhist
Baguazhang is based on Taoist circle walking but the creator is considered to be Dong Haichauan, it is also possible that he was taught this by a Taoist and there are some that say his teacher was a Buddhist.
Liuhe Bafa or Liu He Ba Fa creator I have no idea who that is suppose to be, but it is in principal suppose to be associated with the water exercise from the Song Dynasty and that was supposedly created by a Taoist named Chen Po.
External styles
Shaolin styles are Buddhist and many external styles were influenced by or came from Shaolin.
I am certain there are external styles, or at least one, (the last one I list) that are not considered Buddhist just as Xingyi is internal and not considered Taoist.
A partial list
Buddhist styles are styles that were created or trained mostly within Buddhist temples (primarily Chan Buddhism) or by Buddhist monks, later on spreading out to laymen. These styles often include Buddhist philosophy, imagery, numbers, and principles. The most famous are arts from the Shaolin Temple and descendant arts, like Shaolinquan, Luohanquan, Hung Gar, Wing Chun and White Crane. Shaolinquan places much emphasis on having a balance between the hard (offensive) and soft (defensive) elements.
Taoist styles are styles that were created or trained mostly within Taoist Temples or by Taoist ascetics, which often later spread out to laymen. These styles include those trained in the Wudang temple, and often include Taoist principles, philosophy, and imagery. Some of these arts include Taijiquan, Wudangquan, Baguazhang, Liu He Ba Fa and Huolongzhang.
Muslim styles are those that were practiced traditionally solely or mainly by the Muslim Hui minority in China. These styles often include Muslim principles or imagery. Some of these styles include Chaquan, Xinyiliuhequan, and Qishiquan.
But there is also Shuai jiao the Chinese wrestling art which is believed to have come from Jiao li which was a grappling martial art that was developed in the Zhou Dynasty between 10th and 3rd century BCE. It is considered among the oldest systematic martial arts in the world. I believe its origin is military not Taoist or Buddhist