It was a gradual evolution into the different branches. They generally developed in an area and then spread, gaining influence in other places for various reasons.

There are basically three "denominations" of Buddhism: Therevada, Mahayan, and Vajrayāna. Zen, Pure Land, and other north/east Asian are varieties of Mahayana. Vajrayāna is also sometimes known as Tibetan even though it exists outside of Tibet as well.