What is the difference between Hsing-I, Hsing-I Chuan, Xing Yi, and Xingyiquan?
There is no difference - these are just different ways of romanising the same word in Chinese. The “-quan” or “-chuan” ending is applied to most Chinese martial arts, although it is little used by practitioners as the word “Hsing-I” does not occur in any other context in Chinese and therefore does not require distinction in the same way that “Tai Chi” (a philosophical and religious concept) requires distinction from “Tai Chi Chuan” (a martial art).

What is the difference between Hsin-I and Hsing-I?
Whether there is a difference or not is a matter of debate. Some hold that they are distinct branches of the art, while others hold that any branch of the art can legitimately use either name. The meaning of both names is closely interrelated, though not literally the same. Both names were given to the art by the same person, Master Ji Long Feng.