I cannot find anywhere if "wellington boots" is strictly British term or Americans also use it. Are they called "rubber boots," "wellington boots" or both in American English?
According to the following source they were first made in the UK, but they are now an "international brand."
Hessian boots were unsuitable for wearing under the newly acceptable trousers, so Wellington instructed his shoemaker Hoby of St. James Street, London to modify the popular boot. The result was cut higher in front to cover and protect the knee and had the back cut away, in order to make it easier to bend the leg. It was also cut closer to the leg.
After Wellington’s defeat of Napoleon, “Wellington boots” became extremely popular as stylish footwear that could be worn with trousers.
Initially produced in limited quantities, the popularity of the rubber Wellington boot skyrocketed during World War One. The United Kingdom Office of War hired the North British Rubber Company to produce a boot suitable for the trenches in France and Belgium, and during the course of the war nearly two million Wellington boots were sold to the army.
Rubber boots is the common definition, Wellington is a brand that came to be closely associated with 'rubber boots'. The term is more popular in the UK as far as I know.
Here is one narrow case where google NGrams really shows the difference in frequency well: From Google NGrams Dec 2016
The graph shows that the term wellington boots, which is very specific, is roughly 10 times the frequency in UK books as US books.
What the alternative is in the US for boots that have been made waterproof, there are other more common terms:
- rubber boots or water boots
These seem to be the closest to wellington boots or, more colloquially, 'wellies'.
- duck boots (for a very particular construction kind of boot)
Duck boots are constructed distinctly differently from regular/normal/canonical boots, having a rubber sole and toe/top of foot/heel covering, but with a separate leather ankle lower calf covering.
These (the footwear as well as the term) are common in the US.