Why are certain categories of words more likely to vary between British and American English?

terms relating to cars, trains and roads (boot/trunk, bonnet/hood, railway/railroad, brake van/caboose, points/switches, pavement/sidewalk, road surface/pavement)

These were invented after America was settled and had developed into a large enough community to have its own words. The early settlers had no reason to stop calling a plough a plough just because they had arrived on a new continent (although they might misspell it).
But someone inventing bits of railway technology in America has no reason to use the same word as an engineer in England was already using. Even if, in the days before easy communication, they knew about it.

There are some examples of older English words in America (eg comptroller) that happened to stick because the first settlers used it. Or words from particular regions of the UK that the first settlers came from.

cooking and food terminology (corinader/cilantro, barbecue/grill, grill/broil, /barbecue)

Different immigrant groups. Cooking in England adopted French as the language of sophistication and high class (!). There is no reason why an Italian immigrant to New York should rename their vegetables to the French terms just to copy that

education (university/school, form/grade, invigilate/proctor)

This is more interesting. American higher education started relatively recently from a small pool. A lot of the terms like campus (from the latin for field - because the university was built in a field, but field is a bit downmarket) were simply invented by one person and like all good marketing slogans - stuck.

So terms were copied, whatever Harvard or Yale coined - a new university starting up a generation later is also likely to use to help its credibility.

Communication ease/speed at the time when the terms were invented (computer vs car) or when the speakers separated (education and cooking) should explain it.

The peoples speaking the two dialects split off roughly in the vicinity of the 17th century. During that time intercommunications between them across the Atlantic wan't the best, and remained difficult until quite recently (let's use the year 2000 as a nice round number here).

That means anything that was either developed or undergoing rapid change in both places during those four centuries had to have its accompanying lingo developed relatively independently in both places as well.

So let's go through your list:

• Combustion-based transportation infrastructure: Trains starting in the late 17th century, internal-combustion vehicles around the turn of the 20th.
• Cooking appliances: Early 20th.
• Public education: 19th century.

A particularly enlightening example is actually clothing. The grand champion of messed up meanings is clearly the names we use for articles of clothing. It isn't that we have different names for things that makes it so bad, but rather that we use the same words for completely different articles of clothing.

So how did this come about? Well, clothing certainly existed becore the 1600s. That explains why the words are the same on both sides. But fashion itself is about as rapidly-changing of an industry as can be imagined. So much so that the word has become synonomous with something that is liable to change drasticaly in a short period.