"adjust" means making a minor change or changes to something to make it work better. The word implies that the change can easily be accommodated, like the adjustability is already built in. You adjust your tie, seat, controls, your blinds on the window, etc - all these are meant to be adjusted in the first place. "adapt" means making significant changes, very often to make something fit for an entirely new, unforeseen use. Adapting to a new way of life, for example, means making significant changes to your attitude and habits. In your example, making a normal car usable by disabled people takes a huge amount of work, involving special equipment and professional workmanship and probably needing a legal permit too - it is a major adaptation. Compare that with the usual "adjustments" you make in a car, like setting the seat height and position, the rear view and side view mirrors, and maybe the climate control settings. The two can't even begin to compare.

I was typing out an answer when I came across this link I would recommend you refer to, most notably because the answers are quite accurate: https://www.italki.com/question/144250 Hope this helps.

If that is from an English language test, it's not particularly fair, if it doesn't give you the background information. You would need to know the context as Tony has explained. For example - some cars need to be changed (adapted) so that the brakes get moved so that you can operate them with your hands, not your feet. That's the sort of major adaptation you need.