Shinkansen is definitely Japan's number one method of traveling. Its dense network is covering Honshu, Kyushu and Hokkaido. 31 out of 47 prefectures are having at least one Shinkansen station in their territories.
The difference between Shinkansen and other trains is the ticket gate. Limited express and local trains use ordinary ticket gates of JR but Shinkansen has its exclusive ticket gate which you cannot pass without Shinkansen ticket.
Which means all passengers must have two valid tickets to pass the gate. Basic ticket which is calculated by distance between the origin station and the final destination and the Shinkansen ticket, which is the supplement for taking Shinkansen.
Also you have to keep in mind that basic ticket can be used till your final destination which does not have to be a Shinkansen station. For example, if you are going to Miyajima-guchi station in Hiroshima prefecture from Kyoto station via Hiroshima station, you should have basic ticket from Kyoto to Miyajima-guchi, but Shinkansen ticket from Kyoto to Hiroshima.