Tiantai is a school of Buddhism that emerged in China during the 6th century, founded by the Chinese monk Zhiyi. It is based on the Lotus Sutra, one of the most important Mahayana Buddhist scriptures, and is known for its emphasis on the concept of "perfect and immediate enlightenment."

The relationship between Tiantai and other Buddhist schools is complex and multifaceted. On one hand, Tiantai is considered a distinct school of Buddhism with its own unique teachings and practices. On the other hand, it also shares many similarities and connections with other Buddhist schools, particularly those within the Mahayana tradition.

One of the key aspects of Tiantai is its integration of all Buddhist teachings around the Lotus Sutra. This means that Tiantai does not reject or dismiss the teachings of other Buddhist schools, but rather seeks to harmonize and incorporate them into its own framework. This can be seen in Zhiyi's classification of all Buddhist teachings into five categories, known as the Five Periods and Eight Teachings, which includes both Mahayana and Theravada teachings.

Furthermore, Tiantai also acknowledges the validity and importance of other Buddhist schools, such as Pure Land Buddhism and Chan (Zen) Buddhism. In fact, Zhiyi himself was a student of both Pure Land and Chan masters, and incorporated their teachings into Tiantai. This openness and inclusivity towards other schools is a defining feature of Tiantai and sets it apart from some other Buddhist schools that may be more exclusive or sectarian.

At the same time, Tiantai also has distinct teachings and practices that differentiate it from other schools. These include the concept of the "three truths" (ultimate truth, conventional truth, and the middle way) and the practice of "calming and insight" meditation, which combines elements of both concentration and insight meditation.

In addition, Tiantai also has a unique perspective on the Lotus Sutra, seeing it as the ultimate expression of the Buddha's teachings and the key to attaining perfect and immediate enlightenment. This emphasis on the Lotus Sutra sets Tiantai apart from other schools that may prioritize different sutras or teachings.

In conclusion, the relationship between Tiantai and other Buddhist schools is one of both integration and distinctiveness. While Tiantai seeks to integrate all Buddhist teachings into its own framework, it also maintains its own unique teachings and practices. This relationship highlights the diversity and complexity within Buddhism, as well as the interconnectedness and mutual influence of different schools and traditions.