The first Gradius produced exclusively for a home console, and widely considered one of the best games in the series; however, it was never released outside of Japan. This is also the only Gradius game (other than GOFER no Yabou Episode II on the MSX) where you can select which ship you want to use. Gradius Gaiden includes the Lord British Space Destroyer from Salamander and two (relative) newcomers -- the Jade Knight and the Falchion (a variation of the ship from the NES game Falsion).
There are two variations - the original release, and as part of the "Sony PlayStation The Best" line, which is the Japanese equivalent of America's Sony PlayStation Greatest Hits. This is also the first Gradius game which allows two players to play simultaneously (i.e. allowing two ships on screen). Additionally, it featured the revolutionary Gauge Edit feature, allowing players to rearrange the Weapon Gauge as they see fit.