Tradition is that kung fu was developed in China in the temples. The Bodhidharma created it to teach the Shoalin Monks. Since he was from India, it is believed he combined the arts he learned there with new insights.

Second Answer:

No, Shaolin monks did not create martial arts. In fact, martial arts predate Buddhism (and even religious Daoism) in China by many centuries. The martial arts arose from battles between early people who transformed hunting tools like spears and bows into weapons of war. For most of dynastic China (11th c. BCE - 20th c. CE), military weapons like spears, bows, and swords were used with the expressed purpose of killing soldiers in battle. This emphasis on killing violates the Buddhist precepts against taking life. Most importantly, it is questionable whether the religiously devout monks of Shaolin, which is traditionally associated with the Chan School of Buddhism, ever practiced martial arts at all. Prof. Meir Shahar notes that Shaolin originally took up military weapons in an effort to protect their rich monastery against mountain bandits. They even gained a certain amount of notoriety during the 7th century when they helped future Tang Emperor Taizong (Li Shimin) defeat his enemies, thus allowing his family to found the Tang Dynasty. However, Prof. Peter Lorge suggests that the "monks" who took part in these and later battles during the Ming Dynasty were actually violent men skilled in martial arts who actually dressed as monks to avoid the law or military conscription. It is known that various dynasties had problems with people pretending to be monks. This eventually led to them issuing "ordination certificates" to authenticate a person's monkhood. It is also known that the monks who took part in Ming dynasty battles with Japanese pirates did some very questionable things, like killing an unarmed woman with an iron staff. That doesn't sound like something that a religiously devout Buddhist monk would ever do. These imposter monks were therefore most likely some type of security force hired by the more devote community to protect its interest and to help the dynasty whenever necessary.

For a broad overview of Shaolin martial history see The Shaolin Monastery (2008) by Prof. Meir Shahar. For a concise overview of Chinese martial arts history and a rebuttal to Shahar's claims, see Chinese Martial Arts: From Antiquity to the Twenty-First Century (2012) by Prof. Peter Lorge.

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No, Shaolin monks did not create martial arts. In fact, martial arts predate Buddhism (and even religious Daoism) in China by many centuries. The martial arts arose from battles between early people who transformed hunting tools like spears and bows into weapons of war. For most of dynastic China (11th c. BCE - 20th c. CE), military weapons like spears, bows, and swords were used with the expressed purpose of killing soldiers in battle. This emphasis on killing violates the Buddhist precepts against taking life. Most importantly, it is questionable whether the religiously devout monks of Shaolin, which is traditionally associated with the Chan School of Buddhism, ever practiced martial arts at all. Prof. Meir Shahar notes that Shaolin originally took up military weapons in an effort to protect their rich monastery against mountain bandits. They even gained a certain amount of notoriety during the 7th century when they helped future Tang Emperor Taizong (Li Shimin) defeat his enemies, thus allowing his family to found the Tang Dynasty. However, Prof. Peter Lorge suggests that the "monks" who took part in these and later battles during the Ming Dynasty were actually violent men skilled in martial arts who actually dressed as monks to avoid the law or military conscription. It is known that various dynasties had problems with people pretending to be monks. This eventually led to them issuing "ordination certificates" to authenticate a person's monkhood. It is also known that the monks who took part in Ming dynasty battles with Japanese pirates did some very questionable things, like killing an unarmed woman with an iron staff. That doesn't sound like something that a religiously devout Buddhist monk would ever do. These imposter monks were therefore most likely some type of security force hired by the more devote community to protect its interest and to help the dynasty whenever necessary.

The legend of Bodhidharma teaching medicinal breathing and stretching exercises to the monks comes from the 17th-century. Stan Henning has shown in his paper "Ignorance, Legend and Taijiquan" that the idea of the Zen patriarch teaching the monks boxing didn't come about until the 20th-century.

For a broad overview of Shaolin martial history see The Shaolin Monastery (2008) by Prof. Meir Shahar. For a concise overview of Chinese martial arts history and a rebuttal to Shahar's claims, see Chinese Martial Arts: From Antiquity to the Twenty-First Century (2012) by Prof. Peter Lorge. See also my paper "A Venerated Forgery: The Daoist Origins of Shaolin's Famous Yijin Jing Manual."

SHORT ANSWER:

Basically, it is the difference between an advanced student working toward a comprehensive understanding of the basics, and a Black Belt who is beginning to build on the basics toward a complete mastery of the art. The color belt is a temporary grade level, while the Black Belt is a permanent "Dan" (degree) awarded upon graduation. It is comparable to difference between completing the twelfth grade public education, and earning a college degree.

ELABORATED DETAILS:

In the Korean Martial Art of Taekwondo, the color belts represent the geup (grade) segment of learning the basics from beginner to intermediate to advanced level. The grading system starts with the higher number (either 10th, 9th, or 8th grade at the option of the Master Instructor) and goes down in number as the student is tested, graded, and advanced in rank.

The color belt system is a visible representation of the student's current grade. It begins with the white belt, and each subsequent belt gets darker in color. The number of belts used, and the order of the colors in sequence varies from one Taekwondo organization to the next, but it is the geup (grade number) that is the more pertinent to gauging the student's progress.

The highest grade levels are the 3rd, 2nd, and 1st geup. Most Taekwondo schools use either a brown belt, or a red belt to represent these advance grades, with one, two, or three black taped stripes on the tip of the belt to show each grade. Often times, both belts are used with either the red being before the brown, or the brown then the red. The logic of schools that use the brown as the higher belt is that it is a darker color, thus the last step before the Black Belt. Those that use the red belt as the highest, often use the symbolism that red represents "danger" and the final stage before Black Belt is the most unstable where a student is liable to lose their focus and quit, or character flaws will come out under the pressure of intense training.

One analogy used to describe the grading system in the Martial Art is like building nine story building (since the active Black Belt ranks go to the 9th Degree). The white belt is the starting point where you are doing the most important initial phase of clearing the ground and making it level to start the construction. The architecture of the structure has been prepared, tried and tested by Master Instructors over the years, so all the student has to do is follow the blueprint of training laid out by a qualified Instructor (like the site foreman).

The entire color belt segment is comparable to pouring the foundation. Without a secure and large enough foundation, any future building will crumble and fall to the ground. This is THE most important stage. Upon reaching the 1st Degree Black Belt, the foundation is done, and the walls of each level can be built one at a time until the 9th story is completed through a lifetime of dedication, and hard work.