The main line which runs from Tokyo to Hakata in Kyushu is referred to as the JR Tokai Line and operates three classes of bullet train. These are divided up between the frequencies of stops at intervening stations. Nozomi stops at only the largest stations, Hikari at Large and medium and Kodama stops at all stations.
Although the JR Pass is not valid for the Nozomi and Mizuho trains, you can use the Hikari and Kodama, Sakura, and Tsubame trains without limitations.
The difference in journey time from Tokyo to Kyoto is about 20 minutes with the Nozomi taking 2 hours 20 minutes vs 2 hours 40 minutes for the Hikari. The Mizuho is a new limited-stop shinkansen service operating on the Kyuhu and Sanyo shinkansen lines between Shin-Ōsaka and Kagoshima in Japan as of March 12, 2011.