What kinds of Zen are there?
Forms of Zen can be classified in a number of different ways: by school, by region of China, by country, by period, by speed.
Schools in Zen are largely matters of lineage: dharma heirs of particular masters are said to belong to a school named after the master. Soto is the Japanese pronunciation of a Chinese blend Caodong of the names of two founding teachers: Caoshan Benji and Dongshan Liangjie. Rinzai is Japanese for Linji, a teacher of the 9th century.
Regions of China: Zen of the lineage stemming from 7th century teacher Datong Shenxiu is called the Northern school and that stemming from Dajian Huineng the Southern school. The Northern school went into decline after 755CE.
Countries: Zen began in China, but soon spread to Vietnam, Korea, possibly Tibet, and later Japan. In these countries Zen developed anew, and so we often distinguish Chinese Zen (or Chan) from Japanese, Vietnamese or Korean Zen.
Periods: Zen has changed over time, just like the people who have lived it, and the societies of which if forms a part. Periods of Zen in China are often labelled by the imperial dynasty, so we talk about Tang or Song Zen. In the Japanese context, periods are often named after non-imperial rulers, such as Shogun dynasties. Thus we talk about Kamakura Zen: Zen from 1192 to 1333.
Speed: from its earliest days, there has been a tension in Zen between those who claimed an instantaneous enlightenment vs those who referred to enlightenment as slower. So we sometimes hear of Sudden Enlightenment Zen vs Gradual Enlightenment. The Northern/Southern school split (see above) has on occasion in these terms. Today, some see this difference in Rinzai’s koan and kensho approach, as opposed to the less dramatic serene reflection Zen of Soto.