Only God knows... Perhaps it's carried by horses instead of an engine... :-P ))))
A friend of mine from Athens says that αμάξι is quite an old-fashioned word and it is not commonly used nowadays, αυτοκίνητο is a more common/natural way to say 'car'. Is it so?
I'm a πρωτευουσιάνα like your friend ;-) It's not so old-fashioned, just kinda. It's still used but αυτοκίνητο is more common. Noone will give you a weird look or fail to understand you if you say αμάξι.
Ευχαριστώ πολύ! There are so many things in Greek (as in any language I suppose) that is impossible to learn from books, so thank you again for sharing your native speaker knowledge with us learners!