Sandbox?
My 2 cents...
When I first heard the term Sandbox, it was always in opposition to Railroad. Keep in mind, however, that no matter how 'carved in stone' a label is, there are always going to be variations. It's what happens when you have multiple viewpoints.
So, as I understood a Railroad game, it was generally a pre-made dungeon. In order to get from Point A (the entrance) to Point B (the objective), you had to follow the train tracks. In a 100% Railroad game, that meant you had to go through every room, deal with every trap and fight every monster. If it wasn't a total Railroad game, then you could avoid some of this by taking a different route... or at least encounter them in a different order by taking a different route.
Compare that to a Sandbox: five adventurers meet in a tavern. What will they do? A totally open Sandbox means the players decide what their characters will do. Gather information about lost treasures? Rob the patrons? Etc. A semi-Sandbox will have the GM begin throwing out hints or clues: overhear a conversation about a lost treasure, or a patron wants to hire them to protect a caravan, etc. In other words, the GM offers them options, but he isn't insisting that they take a particular path. Even if they join the caravan, for instance, the characters are free to leave it if something else comes along or the players change their minds.
The Sandbox is the setting. It can be small, such as the Forbidden Isles or the Underdark, or it can be huge, such as the Forgotten Realms or Greyhawk. Even if other fantasy realms are open to the characters (Thieves' World, Dark Sun, Krynn, etc.), I wouldn't consider that an Open World.
What I would consider an Open World is if the characters can go adventuring into other genres, such as Gamma World, Deadlands, Paranoia, Shadowrun or even D20 Modern/Future.
But, as I said, these are fluctuating labels. Railroad, Sandbox, Open World can all have different meanings to different people because that's what they want it to mean. And as soon as you come up with a definition, someone else will publish a game that breaks the mold. Cthulhu is a good example. It can fit into fantasy, Victoriana, modern, and future. So does that make it Open World?
Also, Rifts (Palladium) and Torg (West End Games) are really Open World games.