Ok - so versions of Minecraft:

1. PC Version :  "fullest" version with multi-player capabilities, over the internet playability, modding, posting of videos of your creations & play.  Multiple modes survival (the classic), creative (no threats, build what you want), customizable worlds on hosted servers.

2. A pocket version of Minecraft adapted for play on a Sony handheld.  Limited capabilities.  But the first mobile version

3. Console Version pretty much what it says, playable on teh XBox.. Skin packs available but not much else.  And of course multi-player.

4. Raspberry PI version - uses the popular build it yourself server approach.  Similiar to the pocket edition with limites on functionality.

5. Minecraft EDU - Essentially teh PC version with full capabilities including modding, server hosting, customized worlds, all modes.  Biggest advantage IMHO - easy to launch and run server!  This runs easily on my school network.