Phoebus was driving a fiery car as long ago as the Faerie Queene. Automobile, says Wikipedia, is French. It's more reasonable to imagine that all these terms -- and perhaps others, such as horseless chariot -- were current simultaneously at the very beginning of the motoring era, and that, through the positive feedback loop of popular currency, different ones crystallised into ubiquity in different dialectic zones (the US and the UK not then forming a single dialectic zone to the extent that they do today).

Peter