Buddhism came to China at a time when the intellectuals were hungry for fresh ideas, but it arrived with massive handicaps. It was saddled with the Indo-European focus on an appearance-reality metaphysics and epistemology, with with approximations to concepts of 'truth', sense-data experience, mind as a container of a subjective world populated by counterparts of sensible objects, propositional knowledge, representational belief, a belief-desire psychology together with a logic-informed concept of 'reason' as both a human faculty and a property of beliefs and concepts. The highly developed Buddhist arguments had little purchase on Chinese intellectuals and the only available common form of discourse that could “domesticate” this alien system was Neo-Daoist “abstruse learning” which focused on the metaphysical notions of being and non-being. That issue resonated superficially with a Buddhist puzzle about the nature of Nirvana. If Nirvana was the opposite of Samsara (the eternal cycle of rebirth or reincarnation) then was it a state of being or of non-being? Nirvana is the achievement of the Buddha — the expression of Buddha-nature. So the cosmology of this version of Buddhism, like that of the Neo-Daoists, aided achievement of some goal. Realization of the puzzling nature of this state led to Buddhahood.
Meantime, Buddhism came armed with a paradox that would delight thinkers of a Daoist turn of mind — the fabled paradox of desire. Rebirth was caused by desire and Nirvana could be achieved only by the cessation of desire. That meant that in order to achieve Nirvana, one had to cease to want to achieve it. This argument informs the Mahayana notion of a Boddhisattva, who qualifies for Nirvana but voluntarily stays behind in the cycle of rebirth to help the rest of us. Enlightenment could only be achieved all at once. (This conclusion was also a consequence of the Buddhist view that the ego is an illusion.) The Mahayana wing of Buddhism was the more successful in China because this implicit egalitarianism — everyone could be Buddha, just as everyone can be a Daoist or Confucian Sage.
The other Buddhist philosophy that had the greatest appeal in China was Madyamika, which answered the question of the nature of Nirvana or the Buddha nature by not answering it—Neo-Daoist quietism. The realization of this emptiness was a kind of non-realization, a giving up, or an inexpressible, mystical, prajna-knowledge which contrasts with “ordinary” knowledge. This helped blend discussion of dao and Buddha-nature even more and fueled the eventually widespread Confucian bias that they were the same basic religion.
Meantime, the introduction of a more “Western” religious model (monasticism) to China and coincided with the launch of organized “Daoist” religions. Modeled thus in style and progressively in content, Daoist religion, the quasi-religious Neo-Daoist stoical quietism began to blend with Buddhism.
In China, the two dominant theoretical Buddhist sects reflect the cosmological structures of the two Neo-Daoists. Tian-tai is “center dominated” with a single thought (the inexpressible Madyamika Buddha-nature) determining everything. Hua-yan shifts emphasis to the inter-relations of all “dharmas.” It's a cosmos of interaction that constitutes the expression of Buddha nature.
The most Daoist of Chinese sects is famously the Chan sect. We can understand its Daoist character by returning to the paradox of desire. Laozi's analysis says artificial desires are those created by learned distinctions. If we are to eliminate the desire for Nirvana, it must be by “forgetting” the dichotomy of Nirvana-Samsara. This realization is both the inner reality of enlightenment and corresponds to a mystical answer to the being/non-being of Nirvana. It underwrites the Chan/Zen emphasis on practice, the here and now — “every moment Zen” — and the signature “realization” that we are already Buddha. The Buddha nature is your self-nature—again exemplifying the Neo-Daoist “Sage within, King without” spirit.
Daoist simplicity stimulated Chan's abandonment of Buddhist theory and was accompanied by another traditional Daoist feature — the emphasis on total absorption in practice of a highly cultivated skill. Chinese Zen was dominated by the notion of “sudden enlightenment” which consists of the denial that any process leads anyone closer to the Buddha-nature. You can't get any closer — you're just there.