When role-playing first emerged as a hobby, most games were what are now described as “sandbox style” campaigns. That is, the game master created the campaign milieu as a sandbox in which his players could romp at their heart’s content. The sandbox allows for a maximum of player freedom; they can decide that, today they want to trek to the other side of the planet, and off they go. Megadungeons are often seen as a tentpole feature of such campaigns. Often, the sandbox style of play is seen as allowing the players and game master to explore the world together, according to their fancy.
A plot-driven campaign, on the other hand, is focused on a particular story line. Often, this story is an elaborate affair constructed by the game master, and the players are expected to follow the various clues, visit the detailed locales, and eventually the players experience the triumph of fulfilling the quest (or failing valiantly in the attempt).
This does not mean, as is sometimes erroneously assumed, that the sandbox type of campaign has no plot. In fact, it will often have many plots going on at the same time, running inexorably along their course. What distinguishes a sandbox-style game from a plot-driven game is that in a sandbox the players are free to pick up or ignore the various plots that they uncover as they see fit. In the plot-driven game, there is no game if the players decide to take a course that radically deviates from the plot the game master has devised.
It cannot be stressed enough that neither way of designing a campaign is right or wrong, or better or worse. In such matters of style, it all comes down to personal preference. If the game master and his players simply enjoy the free-wheeling style of a sandbox, or if they love the satisfaction of undertaking a months-long quest with a chance to grab glory at the end, then that style of play is the right one, for them.
Neither style is without its pitfalls, however. The sandbox campaign can, understandably, suffer from a certain lack of connection between the player characters and the campaign setting. Without some sort of meaningful anchor between them, the perils that the players encounter can lack significance unless they are directly aimed at the player characters. And that can get monotonous after a while. Sandbox does not have to equate to rudderless.
The plot-driven game, on the other hand, can fall into the trap of “railroading.” Railroading is a term to describe the phenomenon of the game master forcing the players to follow a certain pre-set course of action through heavy-handed tactics that remove even the illusion of choice on their part. In such cases, the game master turns into a narrator, while the players are simply passive participants. Such heavy-handedness is hardly conducive to a game where the player characters are supposed to be central to the game.
Happy 50th, Star Trek - I was just a bit too young to remember watching Trek when it was in first-run on television (but I was alive then, and it's certainly possible that I was ...