Maybe this is a regional thing, but I'm British and I'm not sure I've ever heard a first language British English speaker use the word "auto" for a car. I'd have said that was purely an Americanism.

I concur - native en_GB speaker here. Auto(mobile) is probably avoided as a general synonym for car because we use "automatic" to differentiate from the default "manual" AKA "stick-shift".

Having said that, this is probably only modern usage. The AA (Automobile Association) and RAC (Royal Automobile Club) both feature "automobile" in their names and are both well over 100 years old.

I suppose (without doing any research) car is probably short for carriage.

I think you're right. I am dual nationality US/UK so sometimes I tend to cross my metaphors. Perhaps a better, British example would be the word "motor" instead of "auto". Used in words like "motorway", but I've never heard anyone actually use it to mean "car" outside of 80s cockney rap.

(Which is apparently a thing: https://en.wikipedia.org/wiki/'Ullo_John!_Gotta_New_Motor%3F)

Nah, still pretty widely used in certain circles - even to the extent that you can have a car sales site called motors and it be obvious: http://www.motors.co.uk/

Well that's certainly an interesting example - that website uses the word "car" in every instance except the domain name.

I think as a usage it's regarded as vaguely old fashioned and twee.

For comparison here's https://www.mobiles.co.uk/ - again, in every instance the noun is either "phone" or the fully qualified "mobile phone".

I've most commonly heard motor as referring to an engine (UK english). I'd say a good example might be from french, with the formal and correct "voiture" not commonly being used, with the less formal "bagnole" being much more common.

Motor is the only word used for engine in Swedish, I believe it's the same in other nordic languages.

I've heard "motor" used quite frequently for "car", but only ever hear it from my 70yo father now (UK English).

I'm a native speaker of American English (California dialect) and I have never heard another native speaker use "auto" for a car except in the context of "auto dealership".

I think you misinterpreted the point. As I read it, "car" and "phone" are the terms Americans (and others) use, and that the British sometimes used "auto" and "mobile" but that usage is dying out (which doesn't conflict with you not having heard it).

As an American, "car" and "phone" are definitely the norm. The only time I've ever heard "mobile" is as a prefix to phone, so "mobile phone". It's sometimes used on forms to distinguish between home, work and mobile numbers (like I just did).

"Auto" maybe but "mobile" and "phone" are definitely equally used synonyms along with "mobe" in all the areas of the UK that I have been to (most).

"Landline" is seeing a resurgence as general parlance for the thing gathering dust, which used to be simply _the_ phone.

Much more likely to say "motor".