Tokaido Shinkansen is the oldest and busiest Shinkasen line and it is operated between Tokyo, Nagoya, Kyoto and Osaka. Sanyo Shinkansen is operated between Osaka, Okayama, Hiroshima and Hakata (Fukuoka). Both lines are connected each other. Many trains, “Nozomi” that is the fastest train on Tokaido-Sanyo Shinkansen, run from Tokyo to Hiroshima and some of those run to even Hakata.
Most of Hikari run between Tokyo and Shin-Osaka, But some of those run to Okayama and Hiroshima.
Sanyo Shinkansen connected to Kyushu Shinkansen at Hakata. Many trains, Mizuho and Sakura are operated between Shin-Osaka and KUmamoto or Kagoshima-Chuo directly. Please see the post, Kyushu Shinkansen to get details.
“Fujikawa” is operated between Shizuoka (=静岡) and Kofu (=甲府) via Minobu line (=身延線). If you go to Mt. Fuji (=富士山) from west side, this train takes you to the gateway stations, Fuji or Fujinomiya. And also this is a short cut route from Shizuoka to Kofu. If you want to go to Matsumoto, Kobuchizawa or Lake Suwa from Shizuoka, ride on this train and transfer to Limited Express Super Azusa or Limited Express Azusa. This train is fully covered by Japan Rail Pass.
When you go to southern part of Nagano from Nagano, the Limited Express Azusa is most convenient choice. You can get Matsumoto directly. And one trip of this train takes you to Hakuba and Shinano-Omachi directly.
The Limited Express Kaiji runs on the same route between Kofu and Shinjuku/Tokyo.
And the new train, “FUJI EXCURSION (Fuji-Kaiyu)” has been introduced in March 2019. This train connects Shinjuku and Kawaguchiko (Lake Kawaguchi at Mt. Fuji) directly.
I will explain you the route, schedule and accommodations of these trains.