I would interpret "performance car" as meaning virtually anything on 4 wheels that has good, on paper performance stats, e.g. high top speed, good acceleration etc. As such, I'd even include some cars that are probably pretty rubbish at handling. So for example, some of the BIG mercs are very fast in a straightline, and I'd call them a performance car.
Can't say I agree with your comment about "sports car" though, and including a whole bunch of hot hatchbacks. My view is that a sports car should be light, preferably front engined, rwd and not have a roof. So I'd classify a Boxster as a sports car, but a Cayman as a "sports coupe".