There is a massive difference. The GM is not a player in the typical sense. He is a special player with a special job. This enables the other players, those running characters, to do so from a pure actor stance. Meaning they do what their characters can do and this is deeply satisfying for some people. It feels more real and more immersive.
This is a fairly false distinction. The GM is special because you've assumed that special role, largely because it works well with some systems, not because GM has some kind of inherent specialness. Once we get to the point that the specialness is assigned, and understand this, we can then actually look at how that works rather than stopping at "GMs are special." They really aren't, they're still players in the game, albeit with differentiate roles. And those roles don't tell us anything about the difference in the fiction created except who creates them, which, as I just covered, isn't something inherent.
And, as for actor stance, the players in the secret door example I gave were entirely within actor stance. Saying, "I search for a secret door," is right there in actor stance -- the PC is really hoping to find a secret door to escape the guards and is trying to do so. The difference is the outcome of this, which, for the player, is still largely the same -- the system is engaged and the result says whether or not you find a secret door. The real difference here is that, in the first example, that system is "the GM decides according to what they think it should be" and the second in "the mechanics decide." The players don't step outside their characters in either.
And while in theory, I don't dispute it's possible for everyone to be authors in a roleplaying game and it be believable, I don't feel that it is that way in practice. At least not to me which is why I use the language I do. If I know as a PC that I'm creating something that is not there yet, I am pushed out of my character viewpoint. You may not be but I am.
To be blunt, again -- given you've no experience with other modes of play, what you feel is true is largely irrelevant. People with that experience and who still use both approaches are telling you that this is not correct, but you persist, arguing from ignorance with assurance.
And, to be blunt again -- it's perfectly cool to never, ever get that experience. It's perfectly cool to be super happy with how you play and not want to bother with another system or think that you wouldn't like it anyway. 100% hunky-dory. It's the claims that your method produces a specific result that other methods cannot that's the issue -- you've zero evidence or experience to make this claim, but persist in the face of people that do have both saying otherwise.
It's very much like five authors saying they are going to write a novel together. It's possible it would be a great novel but the likelihood is low. Passing the creative wand if you will from hand to hand will lead to inconsistencies and shallowness in my opinion. Because creating things on the fly for even one person is hard to do well. The GM is not creating things on the fly or at least not very much at all. He is spending time in advance and he can revise as he goes. I don't know how many times I've revisited my map and revised it or moved a city before the game starts. I don't think I could do it as one person let alone five people most of whom aren't nearly as committed to the game as I am.
It's not like writing a novel together at all. It's a completely different thing.
Now having said that, I am happy if it works for you and I am not denying your experience. You should not deny mine. I think you will find a lot of people that use the exact same language because for them it is true as well. A world created on the fly is just not possibly as good a world as one done in advance. We are mortals.
But, you are denying my experience. Just a few pages ago you were broaching the question if my experience even counts as an RPG! Meanwhile, I have 100% been consistently saying that you have a 100% valid way to play, a fun way to play, that I've both played that way and will probably do so again (feeling a hankering for a hexcrawl starting to lurk), and that there's zero wrong with playing this way. The only denying is coming from one direction, and it's not pointed at you.
Has there been some blunt discussion of how play operates? Sure. Can this be uncomfortable? Absolutely, any good criticism should be uncomfortable or it's not doing much. I'm running 5e right now, hugely closer to your preferences than a game like Blades in the Dark. Everything I've said applies to my own play, and I'm not the least bit upset or sorry about that -- I've embraced this, looked at how it works, and decided it's just fine for me. I will use this approach when it suits the goals I have for that game, 100%, without reservation. And I'll also freely admit that I'm currently running a hard railroad, that play is about discovering what's in the notes, and that there's pretty much zero protagonism in my game. And we're having a blast!
So take this to heart. I am not trying to offend you and I am very much doing my best not to interpret what you say as you trying to offend me. When you deny my own experience of a game though, you really should just speak for yourself. When I say something is immersive or shallow, I am speaking for myself. I am happy the hobby is broad and people engage in all sorts of ways. I am fascinated by some of the rules systems you guys develop. I just don't have the time or commitment to play that way for long.
I'm not denying your experience. I'm saying that when you say that your approach gives you X, and you can't get that any other way, that's incorrect. If you say that your approach gives you X in a way you prefer, I'll applaud that you've found the right way for you to play to maximize fun! And, I'll still talk about how games work.
Fine, that is your take but I've clarified what I mean by a living world. If you read
@Bedrockgames above, he has the same take. It has value to me and my players. YMMV.
I'm had Bedrockgames on ignore for some time, largely because I got tired of the constant accusations of attacking him, personally, while he's busy attacking others, personally. So, no, thank you.
That your approach has value to you and yours is beyond question, and I've never questioned it.