The 'Dō' 道 arts of Japan and 'Zen' 禅

Zen 禅 is a form of Buddhism that arrived in Japan from India as Dhana via China as Channa. The Japanese version of this is Zenna or Zen.

Dhana is a form of Buddhist meditation, absorption meditation to be precise. It is said by the Zen Masters that this is the meditation Shakyamuni Butsu (The founder of Buddhism) experienced to awaken to the true nature of reality.

As Dhana traveled through China it absorbed much of the Chinese thought, especially the principles and language of Taoism. It is this mixture that became Chinese Channa or Chan.

The same happened in Japan with the Descendants of Dogen Zenji (the founder Soto Zen in Japan), when they mixed and merged the Chan with the existing teachings of Japanese thought. It is this combination that we now know of as Zen.

The 'Dō' 道 of Japan is the Japanese pronunciation of Chinese Tao 道.
The dō existed in Japan along with Confucianism and Buddhism in Japan since the 6th Century AD. But these Taoist aspects played a minor role until Zen came to Japan. The dō arts of Japan reflect this influence of  Zen on the arts.

This is most easily seen as the role Zen played in reviving the sacred portions of arts like Calligraphy, Flower arrangement, Tea Ceremony and the other arts the aristocracy were playing with. The Zen monks interacted very strongly with the Warrior Class of Japan as well; and influenced their understanding of the world greatly.

Especially after peace time during the Tokogawa Shogunate...