The fast heating is due to the size. A fan forced oven is the same tech but slower due to being larger. Nothing more.
So if you are buying a large air fryer that's essentially a fan forced oven i have to ask "why not use the oven?".
There may be a case that there's better circulation in most air fryers vs most fan forced ovens. In fact that's true in my case as my large oven and my air fryer have fans the same size (so more relative circulation in the smaller air fryer).
But they are the same tech. The difference in relative fan size probably has some effect but it's not a rule, it's really just a case of how big the fan in the device is and you may have air fryers with smaller or larger relative fan sizes and ovens with smaller or larger relative fan sizes.
If you're wondering why ovens now have 'air fryer' mode that's because marketing. I suspect it spins the fan a little faster.
From what I can tell (and the detail provided on this is sketchy) differences include some or all of (varying between models):
1. Different fan position vs. ovens without air fry mode,
2. Faster fan speed in air fry mode,
3. Using “true” or “European” convection (heating unit behind the fan) in air fry mode, rather than “American” convection (bottom heating unit plus forced circulation fan), which may or may not be used in “convection” mode in a convection oven with an air fry setting.
I haven’t looked, but I wouldn’t be surprised if more peak output from the heating element was part of air fry settings, especially the ones where that is specifically marketed as, or has an additional mode for, “no preheat” air frying.
But of course, up the fan speed and the element size in relation to the interior volume, and make sure you place everything to get optimal air circulation and turbulence (my air fryer has several aero-vanes in its base to create turbulence in the air cyclone, and push it up through the bottom of the food), and you can make an oven that does what an air fryer does.
Air fryer is called "fryer" because of the basket comparison to an oil fryer.