When comparing the differences between Grand Tourers and Sports Cars, from a streetable aspect, it all comes down to size, power delivery, and suspension. A "GT Car" envisions somthing big (not massive, but big), powerful and having a more cushy suspension. Think Maserati's. Sports Cars tend to have stiffer suspensions, be smaller or more geared towards a chassis/body that's function over form (the aerodynamics on a corvette, which are aesthtically pleasing are really there for performance reasons, i.e. downforce, drag, handling, etc.).
Examples (in my opinion) of a GT Car:
Bentleys, Rolls Royces, Maserati's
All powerful cars, no one can deny, but meant for a more comfortable experince
Examples of a Sports Car:
Corvette, just about any Porsche, Ferrari
Cars more aligned with a track enthusiast which can remain streetable