A Sandbox is literally just that, an environment you can play and make things with.
A Sandbox Game is that to some extent, PLUS other tools you can also play with and use in a flexible way. Such as combat and AI controlled environment
Minecraft does not have many additional tools, and therefore I would class it as much closer to a Sandbox than a Sandbox Game.
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As to what there is new or controversial in my post worth commenting on... well, I would crystalize it thus: The Sandbox MMORPG concept is perfect, and the only problem with past implementations is that too many fundamental mechanics of the game were badly designed and not accessible enough.
I am currently running what could be considered an ultimate sandbox: OpenSim.
This is just a virtual world server that is like Second Life (it is based on the code for second life that was released as open source). You have to make everything. However, there is no Game-play in it (other than what you make yourself). It is also multi-player so you can play over networks too.
The above might not on the face of it seem very comment worthy, controversial, or new, but why then have those mistakes been repeated for every Sandbox MMORPG so far?! I can't imagine it being an impossible or even improbable extra effort to implement smooth versions of basic mechanics, and want to know introductions to said mechanics.
I think the mistakes that are made with Sandbox MMOs is that they treat them like regular MMOs but the player does not have to follow the story line if they don't want to. In most MMOs the players are PvE, which means that they are driven to interact with the environment and interacting with other players only comes about due to the difficulty of the dungeons (as multiple people are usually needed to defeat the enemies, especially bosses), but in a Sandbox MMos, the environment does not have any clear direction to it and the players can get lost or leave for lack of direction.
What is lacking is motivation to do something in the game.
The way to solve this problem is to think about the game differently. The main driver can't be pre-set quests and the quest givers, so the only thing that can really do this is other players. IF you just apply the old MMO model of player interaction, there is nothing they really need to communicate about. A player might need someone to help them through a difficult area, but the motivation for doing so is sole dependent on the player in a Sandbox game. Thus only the player who enjoy grind for the sake of grind will end up driving the game experience, not something that really works.
The idea then it so increase the depth and breadth of player interactions. Allow players to set challenges for other players and have the winners rewarded. This does not have to be that players create the areas, but it could be that there is some metric that players can gain by setting goals.
One example is that players can swear fealty to other players and can own land. The maximum amount of land you can own is dependent on how many vassals you have, the more vassals, the more land (although it does mean that you actually own it, just that you can own it).
Players can give other players missions to fulfil, such as attacking another player's buildings as quests. The player setting the quest identifies the location, the bounty that is rewarded for completion and the time frame the mission needs to be done by, and the game determines boss monsters and minions of the place. When another player take up this quest, and completes it, that player is rewarded by treasure and other resources and the player setting the quest is rewarded by capturing the location as their own and gaining some other resources (eg: prestige, etc).
The game-play between the players engaged in the area domination causes the story of the players playing the hack and slash to have motivation (quests). However, the skill that these players have in completing the quests feeds back into the game-play of the Area domination game to resolve their actions. Because of this, it is in the interests of the Area Domination players to provide the Hack and Slash players with interesting and fun quests as that will keep the good players around their areas, but as these will be inherently risky quests (but not too risky), then the Area Domination player must balance the risk against the ability to hold onto valuable players. It creates a complex interaction between both types of players that drives them to create more and more interesting game-play (as the Area Domination players are really competing for Hack and Slash players).
It is a sandbox game as there is not developer created missions, and player are really free to do what they want. Players would be allowed to be both Hack and Slash players and at the same time Area Domination Players. They would be free to spend as much or as little time on either as they see fit (or not player one or the other). However, the game-play is still focused and players would have direction and motivation at all times.