One area that is a particular source for cultural misunderstandings in relation to British and American differences, that I’ve noticed as an expat living in Florida, is in regard to understatement and overstatement. Most countries of the world tend to say things pretty much as they are, but people in the UK and USA tend to distort reality in different directions by the way that they express themselves.
In the UK the tendency is to understate, with the implicit understanding being that the real importance or gravity of what is said is implied by what you’re saying, rather than it being explicitly stated. For example: “I’m feeling a little under the weather” can actually mean: “I am totally suicidal” in the UK, and “We had a very nice day” can mean “That was the most amazing and wonderful experience of my entire life”.
Americans, on the other hand, go the complete opposite way, using large amounts of superlatives and hyperbole, even in what can seem to a Brit like very trivial and mundane situations.
There are differences in body language and gestures too. I remember watching Bill Bryson on British TV talking about the difficulties he had as an American moving to Yorkshire, England. How at first he thought people were being offish with him and he felt like an outsider, until he realized that, as an American, he was looking for much more showy and demonstrative signals, whereas British communication is more reserved and subtle. An enthusiastic American wave, for instance, translates as a few fingers of a hand being tilted up slightly from the steering wheel of a passing neighbour in their car, or a slight nod of the head.
My problems are entirely the opposite, of course. Americans often don’t appreciate when I am complimenting them, because I do it in an understated way – in fact, they can wrongly get the impression that I am being lukewarm or averse, when the opposite is true and I’m actually enthusiastic. On the other hand, when an American comes out with lots of superlatives and hyperbole, I suspect them of being sarcastic, when it is actually a genuine expression of their thoughts and emotions (even if a little exaggerated to my British ear).
It’s a matter of conjecture, of course, but I suspect that most human beings are actually pretty similar beneath their cultural dressing and the negative stereotypes that the British are “cold and aloof” and that Americans are “false” are largely based on misread signals. It can be difficult to tell if a British person likes you because they don’t tend to be demonstrative. On the other hand, an American can appear very warm and friendly, but it really doesn’t mean anything serious.