What is the relationship between Buddha and Tao?

They are two different religious systems, which started at about the same time, but one originated in India and the other in China. In the traditional culture of China, Taoism, together with Confucianism and Buddhism, is a dominant theory and a way to cultivate immortality.

Taoism is a native religion in China, with "Tao" as its highest belief. Taoism, the concept of China's ancient worship of ghosts and gods, is based on the thoughts of Huang and Lao Taoism, and has inherited the immortal magic since the Warring States Period. Buddhism has a history of more than 2,500 years. It was founded by Gautama Siddharta, the prince of the ancient Indian kingdom of Kapilovi (now Nepal) (see Buddha's birthday).

Extended data:

Taoism in academic circles now refers to the ancient religious beliefs in China, which inherited most religious concepts and practice methods of Fang and Huang, as well as folk belief in gods, and gradually formed the highest belief of "Tao".

It is a kind of China religion with Taishang Laojun as the leader and Laozi's Tao Te Ching as the classic of cultivating immortals, but it is not the main classic of cultivating immortals. The main methods of Taoist immortality can be roughly summarized into five types: taking immortal medicine, external alchemy, refining qi to lead the way, practicing inner alchemy, practicing immortality through Taoist utensils, and self-cultivation. Most of the later immortals were cultivated by Neidan.

References:

Taoism-Baidu Encyclopedia? Buddhism-Baidu Encyclopedia