"Album Version" is the one that appeared on the Batman & Robin soundtrack, the first album that it was released on.
"Short Version" is basically the Radio Edit, and the version used for the music video.
"Long Version" is the long version of the short version.
You could also consider it the proper Single version of the song.
BF contained an edited version of the "Album Version" due to CD time constraints. The full 10:23 "Album Version" reappeared on 1992-2002.