This has more to do with human physiology than anything. The vestibular system in the inner ear is what tells your brain motion signals, so to say. The fluid in the vestibulars moves around the 3 axises with whatever environment you're in, and sends the corresponding message to the brain about how you're moving about an axis. This is very much tied into sight, as combined sight and vestibular movement, the brain will interpret exactly where it is in space.
Relating to the example OP provided, movement in cars are typically more abrupt than a transport pilot would typically make. That same transport pilot is also flying the aircraft on autopilot most of the time, which further makes things smoother. Inputting a turn into an autopilot usually creates a very smooth, predictable, flat turn, thus resulting in the sensation that it didn't actually occur to everyone sitting in the back - especially with limited visibility outside the cabin. Combined with other systems, like yaw damper, the computer systems on most all modern transport aircraft make flight easy and smooth. Not only that, but most flight profiles are rather straight and direct, at constant cruise speed.
In a car, there are almost endless amounts of corrections. Bumps, turns, curves, avoiding hazards, braking, accelerating, hills, valleys, etc., thus making the fluid in the vestibulars constantly in motion. It's no different than being on a long, drawn out roller coaster. The sick feeling comes from the eyes seeing a mostly motionless interior of the car (amplified in the back seat), and the constant sensory conflict between the eyes, ears, and other senses. Other than being in constant moderate or higher turbulence, if you think about it, riding in a car isn't a very smooth task.
As a side note, when training for IFR, you're generally taught to keep your head down and inside because the same car sick feeling can occur because the brain processes motion on the instruments, but you're surrounded by gray. The pilot term is spacial disorientation. If you also start fixating on finding the ground while you're in a cloud, things can go awry awfully quickly if you're not paying attention to your instruments. You're taught to overcome your vestibular sensations and trust your instruments completely. Doing anything else could possibly kill you.
