Gills, the car example you provide seems to assume the car is travelling at constant speed, the chair/elevator, however, keeps on falling = accelerating. A direct comparison is difficult because the car example describes movement along an axis not affected by gravity or any other constant force.
To make this easier, let's assume the vehicle isn't a passenger car but a flatbed truck. Let's say it's travelling at a constant 40kph and you're standing on it. Jump now and you might move back just a tiny bit because of the air resistance, but other than that your inertia will pull you along. However if the truck accelerates at, let's say, 0.2g (1.962m/s²) a 1 second jump will already displace you by that much and that's ignoring any resistance! Obviously when you land you'll still be doing almost 40kph so even though you jumped off the truck just fine, you'll have trouble staying on your feet once you land.
The elevator/chair situation is different though since gravity will still affect you even after detaching yourself from the elevator/chair.