When Heywood Floyd dozes off aboard the Orion, footage of a futuristic car can be seen on his seatback screen. The idea of personal in-flight entertainment on the back of each seat was highly prescient indeed – in our universe they didn’t start appearing until the late 1980s. (though many airlines are now phasing them out since they figure everybody just uses their phone or tablet anyway)
Jerome Agel's making-of book describes the scene thus:
Film crew in Detroit made footage of futuristic car and Kubrick in England filmed an actor and actress in dummy seats. Car and couple sequences were spliced and projected onto television screen.
In other words, Kubrick himself didn’t film the brief clip of the cars, but sent a team to do so. And it's been generally known that the main vehicle was a Detroit concept car, and I've often seen accompanying photos of the GM Firebird IV concept of 1964. But that was a very sleek and narrow car whereas the car mostly seen in 2001 is shorter and rounder.
The sequence on the seat back actually opens with a shot of three cars sitting on a non-descript road, with some futuristic T-shaped structures to one side.
The silver car to the right side of the screen (only its hood is visible) looks like it may have been the Firebird IV. The car to the left looked longer and sportier, and may have been the GM-X Stiletto. The shot then zooms in to focus on the pale blue car in the middle. This small car was the GM Runabout.
The scene then cuts to closeups of a man and a woman talking in a car. It’s funny that both Agel and Douglas Trumbull refer to this footage as a “love scene” since the pair could just as easily have been blandly talking about getting a new supermarket trolley. And they were supposedly sitting inside a car that’s parked in some random airport runway-looking place, with other cars strewn around. Future romance, I guess.
Anyway. All three vehicles were concept car mockups which were displayed at the New York World's Fair of 1964, demonstrating GM’s vision of Cars of the Future. The vehicles are not seen moving in 2001 since they weren’t mobile – they were just fibreglass shells with neither engines nor drivetrains.
The Runabout was a concept three-wheeled car, with a narrow nose and bulbous back, that still looks futuristic today. In true mid 60s sexist tradition, it was specifically aimed at housewives, and included one or two built-in shopping carts/trolleys in the rear. The idea was that the lady of the house would load up the trolley with her synthetic pre-packed groceries at the supermarket, drive home, and wheel everything into her glass and aluminium domed house. So futuristic!
It also had an odd steering control pod with dials rather than a wheel, though how this bizarre thing was meant to work was never really explained.