IMO it has to do mostly with Gforces. No Gfocres in a sim. This also affects the way you brake. Having two feet on both accel and brake in real life could mean you also are pushing the accelerator whilst braking because you are being pressed forward in the cabin. You use feet to press yourself against something when braking whether you realise it or not.
REal life also makes it more difficult to module the brake with your left foot because of gfroces, and if you right handed you probably have a lesser degree of control of your left foot. Braking is also a lot more sensitive in real life than the progressive nature in a GT6 is yet another reason for what you describe.
That's definitely part of it, but there's this feeling that, effectively, my limbs aren't "the same", since the necessary movements don't come to me even when the car is stationary!
It's kind of like when I get back on my bike after not riding it for months, or riding different bikes back to back - I
feel loose and out of control (unless it's a "better" bike), and a little over-confident to boot (especially if it's a better bike), although not usually to any real detriment - it's mainly just a perception.
I expect there's a contribution from the enclosed cockpit in a car, too, it really messes with my senses when transitioning from sims (which I see the other way with people who don't sim race, but drive a lot, they do strange things they probably wouldn't in a real car, e.g. excessive steering lock).
Actually, that makes sense - once I'm used to my bike(s) again, it feels sort of like an "extension" of my body. Rarely, I get this with cars, too (certainly with karts), although I need to know where the limits are for that to truly happen, which isn't really practical on the road, and I don't drive very much anyway at the moment (but the disorientation was there even when I was driving every day).
I think that sense of bodily "extension" is missing for me in sims, and everything is interpreted and processed in a purely visual manner, involving no perception of myself within the virtual car and virtual space (which the g-forces help to cement). That kind of changes the context of my perception of myself, that is my perception of my movements when doing things like heel-toe, since I know I'm not "connected" to anything tangible.
Maybe an Oculus Rift would help establish that "connection"*, it'd certainly justify the investment if it'll help my real world driving ability... Or maybe a track day / driving school session or three.
*This assumes that wearing the Rift, or similar, will initially give me the same "disorientation" I get in a real car in respect of these specific control adaptations, and learning / practising through it will help in the real car without, you know, danger.