There are mainly steamed green (Japanese) and fried green (China and Korea). Steamed green is one of the earliest way of making, starting from Tang/Song dynasty...custom of drinking tea went to Japan during that time..so they have maintained the old way ever since. Frying green is developed since Ming dynasty..founder of Ming thought old way of making tea is too delicate and takes time..so he wanted to reinnovate.
Chinese tea basically has 2 types - Chao Qing (fry-green) and Hong Qing (bake or roast-green)
Chao Qing green is done in wok...Long Jing of Zhejiang province, Bi Luo Chun of Jiangsu, Xin Yang Mao Jian of Henan, Zhu Ye Qing and Meng Ding Gan Lu of Sichuan etc belong to that.
Hong Qing green is first done in wok then baked by fire again...Huang Shan Mao Feng, Tai Ping Hou Kui, Liu An Gua Pian of Anhui province etc
Japanese green is steamed green..from Sencha, Gokyuro to Matcha. And there is much more to these of course...