Does anyone know the etymological history or the reason behind the different names that British and American speakers use to refer to the automobile's largest storage receptacle, or more plainly, the boot or the trunk? Perhaps a prominent company's advertising or a prior related usage on either side of the Atlantic influenced this divergence?
The vocabulary applied to today's cars draws a lot from the vocabulary applicable to horse-powered vehicles. See for instance "Limousine", "Berline" in French and other languages or "Cruscotto" in Italian.
In the case of the English "boot", the origin is that in the 18th and 19th centuries, the coachman used to sit on a locker where he could store, among other things, his boots. For this reason, this was termed the "boot locker" and after a while an additional compartment situated at the rear of the coach was used, also called for the same reason the "boot" (for short).
Boots of course were mandatory in those times given the state of the roads. Jane Austen alludes in several of her novels to the fact that speaking about the state of the roads was as common place in England as speaking about the weather. For one thing, the roads have improved since Jane Austen ;-). As for the weather...
As for the American "trunk", well it should suffice to look at all the classic cars designed in the post WWI era, for which trunks were mounted at the rear end.
In this affluent era, cars from manufacturers like Duisenberg, Cord, Buick, Lincoln were all competing for high end customers and these trunks featured many compartments for plates, whiskey flasks and all the paraphernalia needed to go for a picnic. Some cars (mainly coupés, or "roadsters") had special compartments for golf clubs.
In France a similar process lead to people saying "La malle arrière" (as in Louis Vuitton's piece of luggage) and now "le coffre" (the trunk), or in Spanish "el Baul" which is a large piece of luggage as well (and now a more simple "la maleta"). Same for Italian "La baule" which is both the boot or a chest (la baule da marinaio).
The fact that a trunk is a word for a large wooden chest suggests that some of them were carved out from tree-trunks as it is still sometimes found to be the case in some Asian countries were these items, lavishly decorated, are regarded as luxury items (and priced accordingly).
Further back in time "trunk" comes from Latin truncus, or "cut off" → truncated, as the trunk does to the end of a car.
Alain has given an excellent response on the etymologies of boot and trunk. As to why different terms are used, it is simply due to the fact that the cultures of Britain and American having a low level of interchange in the 1780-1950 period (while each was highly interconnected within themselves). During this period, developments called for expanded vocabularies, and the new word uses developed separately in the separate cultures. One place this process is mentioned is in this Wikipedia article, where it says:
What usually happens is that someone basically gets the drop on anyone else when attempting to introduce a new term. Up until that happens, the term would be basically unknown, or there would be several terms for the same thing. Then someone manages to make their preferred term widespread. For a car term like 'hood', it would likely be the result of marketing material across a wide area. Now many more people have reason to use the term and the one they're taught is that one.