I think you hit the nail on the head, Moraline.
I also think there is a very big difference between three aspects of GMing; Defining the world, defining the story, and defining the details. (I'm typing this up for anyone who might be new to GMing reading this, by the way).
1) Defining the world is a basic requirement for any RP. The players need to know where and when their characters are, what the technology level is, how they are to interact with the environment, etc. In a sandbox RP this needs to be defined in much more detail that in a directed RP, as in a directed game, the GM can reveal aspects of the world as the story unfolds, whereas in a sandbox, the players need the information up front to avoid continuity errors.
2) Defining the story is not generally part of a sandbox RP. While there may be subplots that the GM wishes to initiate, they will generally be used to kick-start the game if it begins to flag, or to allow players to keep their characters involved. In a directed RP, defining the story is essential from the beginning so that players know what they are getting into, and so that the GM has a plan to follow. That doesn't mean all the twists and turns should be laid down and set in concrete, of course: that's no fun for the players. The GM needs to be able to adapt the plot to whatever the players do. But the overall direction the RP is intended to go in should be pre-defined so that people know what they are trying to achieve.
3) Defining the details of the world is a totally separate issue from the above. I'm going to use different examples from the fire extinguisher above, one of which Ebb should recognise.
3a) A team of mercenaries is breaking into a heavily defended building. Do you, as GM, define every last little detail of the alarm systems? Personally, I would rather leave that level of detail to the player who's job it is to crack them! This is an example of a directed RP where defining the details is left to the players. I have, however, specified that once a post is replied to it becomes canon and may not be edited, thus a detail, once defined by a player, is set in concrete, even if this later causes problems!
3b) On the other hand, a group of convicts have been transported to an alien planet, where they are to mine a mineral for the rest of their lives. I have described in great detail the mine, the haulage system, the clothing the prisoners wear, the housing, and even the native life forms. The reason being, I have a very specific world in mind and a very specific dynamic I wish to create, so while this is a sandbox (or should that be "icebox"?) roleplay, I don't want players suddenly inventing details that could totally alter the setting.
I think, to be honest, that minor details like the locations of fire extinguishers are more important in a sandbox RP.
Of course, my experience is relating entirely to freeform. System play would be somewhat different I imagine: The player enters the room, (roll dice) finds a fire extinguisher and grabs it, races to where the awful green things are invading the ship , presses the plunger (roll dice) only to find that it fragments the green blobs... (Roll dice) into six!
(Hmmmm - idea....!)