Here's a great definition of sandboxes and themeparks from Stargrace at MMOQuests.com
A sandbox MMO is a game that drops you into a player driven world. Players are given tools, and sand, and they get to make whatever they want with it. just like when you were a kid in your sandbox with a shovel and pail. You didn’t have much fancy stuff, but you had fun.I begin to realize that to some extent, sandbox is about building things, be it ships, houses, or whatever. While I agree that WoW is a Themepark, and more so with each ex-pac, I liked the way you could go wherever you wanted (at the appropriate level) in vanilla, (i.e., Dwarves in Teldrassil) if you were willling to make the effort.
a non-sandbox MMO has already made all the fun for you, there is no sand, its a playground or a “themepark”. its not about you creating content, its about having fun with what the devs made. like when you used to climb around on the monkey bars or whatever.
I think that many themeparks have an element of sandbox in them. I like being directed a bit and as to where I should go to find some adventure, but I think being able to have a home base or outfit I can really call my own is great for developing a sense of character in the game.