I'm running a Neverwinter Campaign Setting campaign right now with no set direction as to where it'll go. It's just got all of the plots and NPCs in the Neverwinter book as background and setting. I asked all the PCs to take themes from the Neverwinter book in order to give their PCs a hook to want to investigate and defeat at least one of the villain groups in the city and I figured I'd sit back and see what happens.
After a session of letting them sit there and doing basically nothing, I decided to go back to my old ways and simply write up an adventure for each session, drop a plot hook in front of them and run what I plan rather than what they plan.
My typical approach is, I think, somewhere between the two approaches you describe. I don't wait for my players to initiate the action - I will frame a situation which requires the PCs to act in some fashion, and so requires the players to choose. And I will try to make sure that, within that situation, is something that speaks to the story elements the players have incorporated into or developed via their PCs.
But how things unfold from situation to situation is in the hands of my players. Which doesn't mean I don't prepare anything - often some courses of action (eg that the PCs will eventually go to the ruined temple to try and recover the lost relic) are fairly predictable. But sometimes things move in unexpected directions. For example, in my previous campaign, before the PCs went to the ruined temple, they got in a fight with a rival clan, and three of them ended up unconscious and shut inside barrels in a storage room in the rival clan's compound. When the other two PCs staged a rescue, the location and opposition had to be worked out by me on the spot.
For this sort of improvisational/just-in-time GMing, I rely on (i) a good general sense of the setting and the genre expectations at the table, and (ii) the game's mechanics working so as to make a situation interesting in play even if it's fairly simple in conception.
To elaborate on (ii), in relation to breaking into the compound to rescue the other PCs. In Basic D&D, if the NPC guards were 5 1st level fighters and the two rescuers were 3rd level, this would probably not be all that interesting to resolve. To make it interesting I think you'd have to pile on more opposition, a more complex floor plan, etc - all stuff that can be tricky to do on the fly.
But in games with more elaborate action resolution mechanics, like Rolemaster or 4e, even a fight with a handful of weak-ish enemies, or the climbing of a wall and sneaking across a courtyard, can become a bit more dramatic in the actual resolution - which shifts the burden away from having to come up with lots of clever stuff on the fly (tricky) and onto making sure the situation unflods (via the mechanics) in an interesting and engaging way (which is the bread-and-butter of GMing, in my view).
To bring this back (at least somewhat) to the topic: my approach to GMing has two main components - (i) setting up the situations, and (ii) adjudicating the resolution of them in a way that maximises interest, engagement, dynamics, driving things forward to interesting new situations, etc. World building I see as secondary - it provides backstory for primary job (i). And settling the rules I see as secondary - it is a subordinate component of primary job (ii).
This is an approach which, in terms of the OP's classificatory scheme, is probably CaS rather than CaW, but I don't think the way the OP describes CaS quite captures the salient features of my approach. It's not primarily about balanced encounters. It's about engaging situations that leverage the action resolution mechanics rather than bypass them.
