Originally Posted by
AlwaysAisle
Kokutetsu Law stated type of train operation and it listed only three: 普通(local), 急行(express), and 特別急行(limited express). Kokutetsu Law did not have such thing as Jynkyuu (準急) or Kaisoku (快速). Was used for service to passengers indicated that a train stops at more stations than express (急行) but still skip stations and faster than local (普通).
The other important distinction is that "express" and "limited express" trains on JR generally have surcharges while "rapid" (kaisoku) trains do not.
On private railways, "express" and "limited express" trains usually cost the same as local trains (e.g. the Keisei "limited express" that goes to NRT and the Hankyu "limited express" trains between Osaka and Kyoto) -- although there are a few exceptions like the Odakyu Romancecar and the Nankai Rapi:t.
And then there are a handful of private railways that have "rapid" (kaisoku) trains, which may or may not be faster than "express" (kyuko) trains.