Short answers, pulled from the story.
Most scholars believe the first schism arose from disagreements over vinaya, the code of monastic conduct, rather than theology. The split divided the community into the Sthavira Nikaya, meaning the Elders, and the Mahasanghika, meaning the Great Community. Most scholars place this rupture in the era just after the Indian emperor Ashoka.
Theravada is the only surviving mainstream school from the early period of Buddhism, derived from the Sri Lankan Mahavihara sect. Its doctrine is based on the Pali Canon, the only complete Buddhist canon surviving in a classical Indian language. It is practiced in Sri Lanka, Bangladesh, Burma, Thailand, Laos, Cambodia, and parts of Vietnam, China, India, and Malaysia.
Scholars estimate that Buddhism encompasses perhaps thousands of distinct sects, sub-sects, movements, and worldviews. The three major branches most commonly recognized are Theravada, Mahayana, and Vajrayana.
B. R. Ambedkar was a modern Indian jurist and social reformer who developed Navayana, also known as the Dalit Buddhist movement. He grounded it in the idea of implementing the principles of Buddhism for the welfare of many people. Navayana's name translates as "new vehicle."
Vajrayana is an esoteric form of Buddhism that developed in medieval India among adepts known as Mahāsiddhas. Its practices include mantras, dharanis, mudras, mandalas, and the visualization of deities and Buddhas. Tibetan Buddhism is its most widespread form, practiced in Tibet, Mongolia, Bhutan, the Himalayan region, and the Russian republics of Buryatia, Kalmykia, and Tuva.
Mahayana accepts a body of texts called the Mahayana sutras, which Theravada schools exclude from their canon. Mahayana schools generally hold that many Buddhas exist in other realms or pure lands as transcendental beings with vast powers, while Theravada focuses on the Pali Canon alone. East Asian Buddhists following the Mahayana tradition constitute over half of all Buddhists worldwide.