Fast road car to me is more power, putting the power down better, better handling and braking without compromising the car on the road. So making it too crashy or twitchy, too loud. So effectively you could still use it every day quite easily, its just faster in a straight line, around bends and coming to a stop.
The next step is road legal track car, stripped out (completely or partially), harnesses, stiffer suspension that compromises the ride quality, noise levels, roll cage. You might use it occasionally but you wouldn't want to use it all of the time.
With mine I'll probably go somewhere in between as I won't be using it daily but I still need some degree of comfort, low noise level and practicality from it.