You are missing my point

No one in the UK (ok, not quite but very nearly) would ever use the word automobile to refer to a car or things related to a car. For example the UK press would never refer to the industry related to personal motor vehicles as "the automobile industry", it would always be "the car industry". Whereas a quick Google suggest that the US press uses the terms interchangeably.

Automobile appears to be a very much US centric term (when compared to other English speaking lands) and I still reckon if as proposed we in the UK had taken our lead on car terms from the US that most of the various terms that are/have been used in the US would also have been common here.