Is every minecraft game for Xbox different?

Yes and no is the best way I can describe it.

With the disc version there may well be different ones. Minecraft updates the game on a fairly regular basis - adding new elements to the game etc. Recently they changed the tutorial world as well as adding forest biomes, ocelots and probably a few other items. The original disc will have the first tutorial but discs bought now have the new one.

However, with older discs, the game will update itself so it will catch up with the new one. However if it is played on a console that never connects to the internet, the old version will be played.

The download version is similar. You get the latest version when you first download then it updates as needed when on a live connection.