^ In a nutshell, yup... So the TommyKaira ZZII or TVR Speed 12 have normal paint schemes (like street cars) but they also offer full downforce tuning (like a racecar). Some drivers would call them racers, others would call them street cars.
Generally when I'm racing with friends, we consider anything with adjustable nose down force as a "racecar" (and thus ineligible for street car races).
For what it's worth, there are a handful of full street cars that will take on (non-adjustable) nose down force from the aero parts in GT Auto (the Aventador is one).
That said, I suspect that our young questioner may be in trouble with his R35. Even after a VCD and LSD tuning a lot of 4wds are still super tight in the corners...