The representative of Confucianism is Confucius, whose English is Confucius, while Confucian scholars are Confucianism, and the whole Confucianism is Confucianism.
Similarly, what Taoism calls "Tao" is translated into English as Tao, Taoist scholars are Taoism, and Taoism as a whole is Taoism. Let us look at Buddhism in the same way. Buddhism means Buddha in English, so Buddhists and Buddhists are Buddhists and Buddhists respectively.
Confucianism, Buddhism and Taoism are the three cornerstones of Chinese traditional culture. Confucianism talks about "joining the WTO", Taoism talks about "being born" and Buddhism talks about "hiding the world". We should aim at becoming "gentlemen" in Confucian cultural education and constantly improve our self-cultivation. Taoism strongly advocates a life style that is natural and good as water, while China Buddhists, represented by Zen Buddhism, understand the true meaning of illusory silence through enlightenment.
To view:
Confucius → Confucianism → Confucianism.
Tao → Taoism → Taoism.
Buddha → Buddhists → Buddhism.
Generally speaking, adding ist after nouns refers to the identity of characters, such as Mohist and Legalist. Plus ism refers to a kind of ism, belief, ism, etc. For example: Christianity, Christian spirit, Christian doctrine.