Installation of Diablo 1 basically only had two options: shareware or full.
Diablo 2 had two "full game" versions possible in addition to the shareware. There was a separate "Cinematics Disc" which wasn't necessary if doing a "partial install" which just meant players could not watch the cutscenes (unless wanting to play them directly from the CD) but could still play the rest of the game. This saved time and space installing the game.
Diablo 3 like many of Blizzard's modern games allows playing games with only a partial install of all files, which can continue to download in the background while the user plays. This applies to both the demo and the full.