I should know the difference between the Indians and the Chinese, since they apparently do not like each other.
Buddhism started in India, but hardly exists there anymore. Brahmanism -- the older Hinduism, left an imprint though.
The older Theravada form of Buddhism spread to what is now Burma, Thailand, Cambodia, Shri Lanka, etc. it absorbed native animistic religions, giving each national Theravada Buddhism a unique ethnic flavor.
The so-called Mahayana spread north into Tibet, China, Afghanistan, Korea, Japan, etc. There it absorbed Bon, Taoism, Confucianism, Shinto, etc. Mahayana gave rise to Zen, Pure Land, Flower Garland, Tiantai, Esoteric Diamond, and other schools of Buddhism.