1) GMing a game to support the setting
2) GMing a game to support the story
Type 1 is characterized as follows:
-Let the chips fall where they may. NPCs have stats, the world has a set of standards, the places, people, behaviours, and world systems in general follow logical arrangements, and don't exist for any further reason than it makes sense. The concept of anti-climactic doesn't exist. If you are lucky to meet the main villain in the first few minutes, ok, if you never find him, ok, if you kill him with a lucky critical, ok, whatever. The setting is set up, the pieces are put into place, and then you hit go. The rules of the game should be consistent. House rules are fine, but they are decided on, and at the end of the day, the consistency of those rules are respected, impartially for players and non-players alike. NPCs grow and get xp like players, to keep them growing in a fair and consistent manner (they might get more or less xp, but they still obey the same rules as anyone else). NPCs can't generally do things contradict the same rules players are subject to.
Type 2 is characterized as follows:
-You've seen the movies, read books, you know how a "story" runs. Villains behave in certain ways. Villains can be beaten, but only at the climactic moment, in a memorable way. Mood, theme, concept governs the expected flow of the game. Games have genres that must be respected. Vampire will be dark, moody, gothic, Seventh sea will be dramatic and flashy. Players can't accomplish big things without some effort, but they can accomplish it. Their goal is never impossible, but also generally not easy. Generally, the climax will not be thwarted. Game rules are generally more flexible. Sometimes NPCs are not subject to the same rules as players...depending on dramatic appropriateness. The rules that players are subject to can also be flexed as the scene demands. GM fiat is an accepted means to an end (though should be used sparingly) if it furthers the dramatic flow of the story. GM may sometimes gently nudge players back towards the expected flow of the story. The story does not have to end, and the climax may well set you on the path of a bigger story, but the dramatic license continues to exist.
Now I realize, it's not type 1 or type 2, and never the two shall meet. Type 1 will still have a plot in mind, will still have NPCs that are interesting, maybe giving them interesting connections to the players. Type 1 will describe things in vivid ways that capture the imagination. Type 2 must still respect the dramatic tension, and realizes that a player must actually risk failure in order to feel that tension. The player that trys to jump a chasm, must genuinely risk falling in order to feel trepidation at trying it, even though we know in the stories, the hero won't fall, though it may get close. Type 2 can't go so far as the players get apathetic because they see that the story is controlling their characters not them. Ultimately, a successful game will fall in between these 2 types, not at either pole.
But how far. Some like staying as close as possible to type 1, some to type 2. Some will vary depending on game. For instance Call of Cthulhu is probably far more often done in the type 2 mold. Something like cyberpunk might be more frequenly type 1. Some GMs will stick with 1 style of the other almost exclusively though.
Personally, I prefer type 2, with enough type 1 that I feel I am still controlling my character. However, since I enjoy the story, I am likely to play my character in such a way as they fit into the story. I've read fantasy books, I have seen movies, I have imagined stories. I like the drama, I like the struggle, I like the climax, I like the poetic license of it all. The hero does not defeat the villain by page 5. Nor does he abandon the story either, not unless something pulls him back. The book simply doesn't finish that soon. Type 2 does sometimes require more mature players. You need players that will make characters that also fit the theme, that won't mind when the setting is leaning on them a bit. The GM must be fair, but the players must roll with things that might seem unfair to a type 1 players. Your big magic sword got stolen. In type 2, the GM made it happen for a dramatic reason, and may or may not give the chance to get it back, again in due course with the story, and the player knows that, and will roll with it.