I think there is a difference. The fatigue point system is saying, "In the game world your guy only has so much energy to use special manoeuvres; we use Fatigue Points to abstract that energy." Fatigue points are explicitly part of the game world.
The way I look at it, the reason fatigue points are part of the world in the first place is clear: to limit the number of times a PC can use their super-moves, ie it's explicitly gamist, and not a modeling methodology.
If you were really attempting to model fatigue, the fatigue system would cover more kinds of physical exertion that commonly occur during combat, like moving/running in armor --and not just flashy combat super-moves-- but that would, I think everyone would agree, bog things down. It's opening a big ole can of worms.
So they're explicitly part of the game world, except in the ways they aren't (when they're just a transparent metagame mechanic). To my mind, they're not far removed from something like AEDU, ie a marginal difference, not a categorical one.
The AEDU system is only implicitly part of the game world.
Agreed. But it's not a big deal for me, personally, and I've never encountered a player whose sense of character immersion, or lack of, was rooted in mechanical minutia -- immersion was always a product of larger-scale campaign intangibles; setting, NPCs, quality of DM, plot.
I've only encountered people like that online

.
For the record, I treat the rules/mechanics as approximations of the in-game world (and not their 'physics'). I start from the assumption it's my job to connect the rules procedures with the in-game fiction. This is how I made my peace with several of D&D's traditional core mechanics, ie hit points, saving throws, Vancian casting.
When I DM, the "reality" of the setting comes from words I speak aloud. The rules are just a bunch of guidelines for resolving low-level actions. They aren't, and aren't intended to be, the primary lens by which I-as-my-character understand the fictional world the game takes place in. The rules are what I-as-a-player need to know, in order to get things done.
Trying to explore the fiction of the game world as a player via the mechanics strikes me as being as sensible as running a painting under an election microscope in order to gain an appreciation of art. I imagine a small, select group of people might find that enterprise terrifically interesting -- but the general museum-going public? Not so much...
I really like the idea a single set of (simple) guidelines (rules) can be clothed in many different fictions -- that way, I don't need to design custom mechanics for each one of my settings/campaigns.
Some powers rely on the players to place them within the game world.
I'd say almost all powers rely on that, regardless of edition.
Try describing how a person with a sword fights a bear or a dinosaur without the players & DM helping out with the fictional positioning, or what a saving throw looks like, or, well, you get the idea.
Come to think of it, I'd say the willful act of 'positioning' the raw output of the game's procedures/algorithms in the shared in-game fiction is a big part of RPG play. A huge part. The rules and the players and the DM are all partners in creation.
I see that fatigue points have that connection baked into the mechanics before play, whereas Come and Get It needs that connection created at run-time by the players.
They're
baked-in... but still
half-baked!

(because they only pretends to address modeling something, ie exertion)
Well now. If that's true then maybe I finally get it.
Cool!
I still think it's a terrible critical framework, but that's mainly because of JA's canny refusal to apply his critiques to mechanics he personally approves of. Well, that and his insistence the close connection between a mechanic and the fiction --without regard to outcomes??!-- produces a stronger sense of immersion.
To which I ask: immersion in what?