So you have, by your example, described what a sports car is as defined in the OED, that is a low-built car designed for performance at high speed. Back in the day, that is the early 1900's the term first started being used in Britain, to describe a racing car built for touring, think early 3.0L Bentley's, they were designed to be driven to a race track, race and drivin home. As the years have passed, the interpretation may have evolved, but the OED's definition, in my opinion, still stands and has little to do with how much a car weighs.I agree that handling characteristics, how driving a car makes you feel, and aesthetics are all key components of what defines a sports car, but the boundaries are now blurred by electric cars.
Handling is governed in part by the car's mass and its distribution, as well as the dimensions of the vehicle including its track and wheelbase, and the suspension set up. When compared with my Exige, my wife's Taycan is 120cm longer and 25cm wider and taller; the wheelbase is 60cm longer and the wheel track 20cm wider; it's 2.5x the mass, yet the handling is just as sharp and nimble. It's stable at high speed in a straight line but also readily changes direction - I can take corners without slowing down that would make me nervous in my Lotus. The centre of mass is lower than the wheel centres and in the middle of the floor of the car. The weight distribution of my Lotus is 60% rear-biased and the centre of mass is around 45cm above the ground with a kinematic roll centre 3cm above the ground. The Lotus has double wishbones front and rear, the Porsche has double wishbones at the front and multilink rear combined with active suspension.
Driving my Exige is raw and visceral at all times, but it is at the extreme end of the sportscar spectrum. The Taycan can be a silent, high speed luxury mile-muncher or transform into a stimulating car with a mind-blowing ability to accelerate, brake and change direction without body roll or loss of stability. There is fantastic feedback through the wheel and the car is easy to place in bends. It lacks the olfactory feedback of a car driven hard, and doesn't reward such driving with ever more dramatic sounds, but it also doesn't deafen me or roast me on a hot day. In most ways, it is far from lacking excitement.
If aesthetics are considered, the aspect ratios of both cars are near identical in terms of ratios of height to width, height to length and width to length. The Exige is a mini Group C racer; the Taycan is a wide, low-slung coupe.
However, whilst the Exige is a undoubtedly a sportscar, most would struggle to use that word to describe the Taycan.
