There are many different schools, or sects, of Buddhism, just like there are many different sects of Christianity. However, all the sects of Buddhism can be categorised in three main streams; Theravāda, Mahāyāna & Vajrayāna. Theravāda is found in countries such as Sri Lanka, Thailand and Cambodia, and this school bases its teachings solely on the Pali Canon. Mahāyāna Buddhism is found in countries such as Tibet, China, Japan, and Korea, and bases its teachings on the Sanskrit Āgamas and the Mahāyāna sūtras. Vajrayāna Buddhism, whilst often viewed as a separate school, is actually a branch of Mahāyāna Buddhism, however it also includes esoteric ritual practices and incorporates the tantric manuscripts in to its corpus.
Tendai-shū is a Mahāyāna school that includes Vajrayāna practices.
The Tendai School of Buddhism was first founded by a monk called Chih-i, in the Chekiang Province of China at the latter half of the 6th century. The sect was named after the mountain on which Chih-i lived, T’ian T’ai Shan or Tendai-san in Japanese. Chih-i was a meditation master, influential teacher and student of the famous master Nanyue Huisi, a leading authority on the Lotus Sūtra and the Prajñāpāramitā literature. He was massively influenced by the teachings of Huisi, Huiwen, as well as the teachings of Nāgārjuna, a 3rd century Indian monk and the de-facto founder of the Madhyamaka tradition of Mahāyāna Buddhist philosophy. For this reason, Chih-i is often considered the 4th Patriarch of Tendai Buddhism.
Tendai Buddhism remained highly influential in China and in the early 9th century, was brought to Japan by Saichō, a Japanese monk. Saichō travelled to China in 804 and stayed at Mount T’ian T’ai. He was taught, and given Dharma transmission by Daisui, the 7th Patriarch of Tendai. Whilst in China, Saichō also stayed in Yuezhou, where he was taught Esoteric Buddhism.
On his return to Japan, he built a temple on Mount Hiei and founded his school of Tendai.
Tendai emphasises the historical Buddha Śākyamuni who represents the exoteric world, and the Eternal Buddha, Vairocana, who represents the esoteric world of the Dharmakāya, the highest aspect of the Three Bodies of the Buddha. Both of them are one and the same. This intergration of esoteric and exoteric teachings led to the establishment of two study curriculi: shikangō which focuses on meditation and the core T’ian T’ai teachings, and shanagō which focuses on esoteric practices. Japanese Tendai also emphasised the Bodhisattva Precepts and embraced elements of Pure Land Buddhism, becoming a rather syncretic school of Buddhism.