Sigh, I think others are making this more complicated than it is and aren't answering the right question.
Perhaps it will make more sense if you restate that brief blurb as:
The players determine what their characters say, think, and do. The GM describes everything else in the world.
You "say" what your character does, the GM "says" (aka determines) what everything else does. That's all that part of the rules is trying to convey to you. It's not making a statement about whether you speak your thoughts out loud or not.
Now for the truly tangential "do you say your thoughts," it depends on your style of game. If it's an in-character type of game you don't, you express yourself as your character would. If it's more storygaming, like in Dungeon World, you can say what you are really thinking, narrate lengthy flashbacks, and otherwise express your character's life of the mind, but this is situational, not stream of consciousness spouting. If you are more of a tactics player in say D&D you may or may not bother with such in-character frippery amidst the "you should flank him to get the extra +2 next round" table talk.
Mind Your Follow-Through
Note that Defy Danger starts out with:
When you act despite an imminent threat or suffer a calamity
Getting rushed by screaming kobold fanatics who've set themselves on lightning* is pretty calamitous, and if you hit on a 10+, that's great! But what it means is that the threat doesn't come to bear right now, not that it vanishes forever - "defy" doesn't mean "eliminate".
Yes, you are encouraged to start setting up the scene with softer moves, but all of these moves are things that are actually happening in the fiction. The players aren't trying to, like, counter and eliminate your moves or anything, they're also taking actions in the fiction and accomplishing their own things. They can manage to be both momentarily safe and still very much in danger.
So, you hit on a 10+. The screaming kobold fanatics haven't gone away. It's just that when the first one rushes into the innocuous-looking jar/carefully positioned Leyden mine and they both go up in a cloud of electroclasm and smoke, you're not right there with them.
Awful lot of jars in here, aren't there?
* no one ever said the path of the blue dragon fanatic would be easy
Mind Your Setup
Tell them the requirements or consequences and then ask is often underestimated, but it's an excellent way to extend the results of moves without having to write entirely new ones.
So if, for example, Stringfellow surveys the upcoming holosparkst, decides it's time for the better part of valor, and says he's diving out the nearest doorway, that does sound like Defy Danger too, doesn't it? But you can always say:
Sure, but things in here are ramping up rapidly. If you make it out, getting back in to help everyone else won't be nearly as easy.
Or:
Sure, but whatever that just kicked off is already cascading around the exits. You'll be taking 1d6 damage through armor just to try.
Or even:
Sure, but, gosh, there's all this smoke in here and your ears are still ringing from the blast. You can get out somewhere safely, but it's not entirely clear to you where that's going to be.
And then end with:
Is that alright?
And if it's not, then Stringfellow isn't going to dive out the door in the first place. His turn in the spotlight will be spent doing something else. And if it is, then even a 10+ on a Defy Danger will still leave Stringfellow in a bad position. It doesn't violate the spirit of the move to do this - accepting those known bad outcomes is just the cost of making the move in the first place.
Mind Your Prep
And, of course, if you knew all along that there'd be kobolds in these ruins and they laid traps like the dickens, you can sit down and craft custom moves to deal with this and take Defy Danger off the table as an initial reaction. Something like:
When Lightning's Claw springs their ambush on you, say who was the most cautious among you and have them roll +WIS. On a 10+, they pick 1. On a 7-9, the GM also picks 1. On a 6-, all 3:
- You're right where they want you. Everyone takes -1 ongoing to all rolls to dodge or escape, until you're out.
- You didn't see this coming. Pick someone else in the party to take the brunt of the first attack; the GM will make a move against them.
- They timed this one perfectly. All their damage is best of 2 rolls, and when they gang up it adds +2 damage instead of +1.
But you don't need to haul something like that out all the time, just for when you want it to be a sufficiently big deal that a regular Defy Danger doesn't seem like it should be able to resolve things satisfyingly on its own.
Best Answer
You're right, how a Dungeon World GM figures out what dangers (if any) threaten the PCs while they're sleeping doesn't work like in other games.
How the GM handles Take Watch is somewhat complex. Let's break it down.
Like every player move in Dungeon World, the Take Watch move is only triggered when its trigger is matched. The trigger is:
This seems to imply that it's up to the GM whether something does or doesn't approach, right? No, actually, there's more going on here than meets the eye. It is definitely in the GM's hands, but how the GM handles this isn't just deciding on a whim.
Having something approach the camp is necessarily a GM move. Since the GM isn't allowed to make a GM move any time they want, if something approaches the camp, it must be via a GM move. That GM move could be triggered by the players all looking to the GM to find out what happens, and that is naturally fairly common when the PCs go to sleep — they bed down, and everyone looks to the GM to start the next bit of conversation.
However, having a GM move isn't enough to always make something approach the camp. Making GM moves is governed by the GM's Agenda and Principles. There are four that are key here:
Make a move that follows
This is the most important Principle. If something approaches the camp, it's because it's already part of the fiction that something would or should. Are they camping in safe, empty lands? It would be inappropriate to make a GM move that makes a pack of growling wolves appear. Are they camping in safe, populated lands? Then it would be appropriate to make a GM move to have a tired fellow traveller approach the camp. Are they camping in unsafe, populated lands? (Has a soft move setting up this fact already been made?) Then it's totally appropriate and sensible to bring to bear the danger of the region itself somehow.
Think offscreen too
This is a secondary source of the GM move that could have set up the GM move that made something approach the light. Did you previous have a player's 6− miss, and used it to decide that there was an assassin stalking them? Well then, if the assassin hasn't already been brought to bear on the PCs before they make camp, it's obvious that when the players look to you to find out what happens during the night, the answer is that the assassin approaches the camp and triggers the Take Watch move.
This plays in tandem with Make a move that follows, because it's a way that fiction naturally develops details that point to the obvious next thing to follow.
Fill the characters’ lives with adventure
This Agenda item means that if the players trigger a GM move, make something happen. Pick a GM move and fulfill it. It doesn't have to be dangerous — just adventure. The purpose of making GM moves is to give the players an interesting adventure.
This is important to keep in mind because it moderates Make a move that follows and prevents it from being dull, repetitive, or predictable. The world should be serving up new and interesting things for you to make GM moves with, or at least new developments that make the same world element show some kind of progression and development. What shouldn't happen is the players make camp 10 times during an adventure and every time a pack of wolves appear because it's “what would follow” from the circumstances.
You should be making moves that follow from the fiction, but the fiction should also be in motion. If it isn't, then it's time to pull in a wrinkle from somewhere else in the fiction to modify the situation.
Keep in mind too that a GM move that adds adventure to camping doesn't have to take the form of something approaching the camp at all! For example, give an opportunity that fits a class’ abilities could equally be “hey Ranger, you're actually feeling pretty rested since you all got a ride on that merchant's cart today and said you slept most of the way. You noticed tracks about a half hour before you stopped for camp, and you can tell this is good land for forage and wild game. Want to go foraging or hunting? It's a moonlit night and you can see well enough with your elven sight.”
Play to find out what happens
This Agenda item is super-important. In a game like D&D, what typically approaches during watch? A combat encounter! But despite its D&D heritage, such a presumption when making a GM move is antithetical to Dungeon World.
It's tempting to assume, as a GM, that something approaching in the night is a combat threat, but playing to find out what happens means that you should avoid this. Sure, maybe its wolves, but don't assume it will be a fight. You could just have wolves attack out of the darkness, but that's trite.
Instead, just present the wolves: there beyond the firelight, a glaring form growls. What are the players going to do? Find out. Yes, it might lead to a fight, but it's already more interesting and allows for more variety of PC responses. Alternatively, have that wolf just walk into the edge of the firelight and lay down, looking at the PC on watch — what do they do? (Both of these are show signs of an approaching threat, to my mind, though the threat of the first is obvious, while the threat represented by the non-hostile wolf is much more ambiguous and likely strange.)
I've found that the best way to play to find out what happens in situations where I'm tempted to assume combat, is to pick the more ambiguous GM moves: Offer an opportunity, with or without cost, for example, or perhaps Give an opportunity that fits a class’ abilities. These don't say “ow, danger” to me immediately, so they're good for countering my temptation to always make moves that are obvious threats. What's more interesting in the middle of the night, yet another wolf encounter, or “Hey Wizard, during your watch you notice a faint blue glow moving through the trees. A moment later it comes out from behind a tree and you see it's just a ball of light, and it's just floating through the forest, going somewhere, passing by your camp. What do you do?”
Conclusion
That's a lot of words to say something relatively simple: yes, what might approach and trigger Take Watch is up to the GM and is revealed with a GM move, but the exact GM move and its fictional content should be based on a firm grounding in what's already been established, and the GM shouldn't presume that it will be a combat encounter.