@mase_aga Depends on the distance. For longer distances (where taking a plane is a reasonable option) there are few non-shinkansen routes that still operate, if any. Sometimes they have sleepers but that's more touristy. It's kind of like U.S., the cheapest option is intercity buses.
The weird thing with Japan's rail system is that since it's all electrified, the "commuter rail" runs trains that are similar to subway cars. The routes themselves though spread all over the place in a massive net. Around Tokyo there isn't just JR East, a lot of other rail companies operate lines. You can take the Skyliner (not operated by JR East) from Narita airport into Tokyo, or the go to Yokosuka on the Keikyu Electric Railway line (also not JR). What we would consider "commuter rail" connects major cities in the region, bringing them closer together. This doesn't really extend to other regions though because of the mountains, so if you want to go to Osaka you still have to go by plane, bus, or shinkansen.