I'll take a shot at it.
Classic. You get to walk/fly around and build. You have access to basic blocks and just the one game type.
Full version: Two game types (three really but two of them are very similar).
Creative: You have access to all the blocks you do in classic. Also you get different colors, textures, fences, doors, paintings etc and there is a lot more that you can do. Also you have redstone where you can make circuits and automate things like doors and pistons.
Survival: You start out with nothing and you cannot generate items (unless you mod or cheat). You have to gather materials to survive. You have to eat, build shelter and fight off/defend against a few creatures. Survival game servers are fun because you get to go on adventures in a sense with other players. Whether it is mining and building cities with others or (if you find a pvp server) build forts and make factions against other players. Defend your stuff and go to war, make alliances, steal peoples stuff. I got into the pvp stuff for a long time.
I believe hardcore is a suped up survival.
Just note that active classic players are kind of favored over survival players on here as much as I hate to say it. The survival server is lightly moderated compared to the classic server and there is no ranking system or chance to climb the ladder.
*but*
Once you buy the game you have it forever. This includes every update and feature they will ever come out with.
I bought the game and had lots and lots of fun for about 9 months before I got bored with it.
