Both schools had Chinese roots. Rinzai is the Japanese transliteration of Lin Chi; the Lin Chi school flourished in China for several generations before Eisai.
Similarly, Soto is Eihei Dogen's Japanese offshoot of the Chinese Caodong school. Before these two, Zen training for Japanese monks meant travelling to China.
Americans originally got a very Nihoncentric view of Zen (Ch'an) from Suzuki and others, but this has largely been balanced out in recent years.
The influence of Korea has largely been overlooked, too, but those remote mountains harbored a tough strain of early Ch'an over the years, and Korean teachers like Chinul would come down every few generations and freshen things up in China and Japan.
> This supplies a more accurate answer to Robert J. Bradbury's query,
> "Would you say that Zen is derived from Taoism?"
Also in the T'ang period and earlier, there was little distinction between schools. Monks from different sects would work and study side by side with each other and with Taoists in the same centers. There are a few stories that involve Ch'an monks with problems going to see their local Taoist sage for some kind of fiendishly clever remedy.
In sum, I'm agreeing that Zen is liberally flavored with Taoism but not derived from it; I'm just wordy :-)
I use this address only when I am away from home. I have reply-to set to firstname.lastname@example.org and I read email sent to that address from here, so please don't use the yahoo address.