The British tend to be far more private (and much less arrogant) as a culture than us in the US.
We tend to use the description 'reserved' (at least my age/social group do).
Your observations about the differences between us pretty much mirror mine from living in central Iowa in the '80s and central Texas in the early '90s.
It used to amaze me when I was first in the States that I could meet a total stranger in a bar and within 10 minutes they were telling me things about themselves and their lives that I wouldn't share with anyone who wasn't a pretty close friend.
Correspondingly I got accused of being unfriendly, cold or aloof because I didn't treat people I'd just met as though they were lifelong friends.
In the '70s and early '80s the Brits tended to find the Americans loud, lacking in manners, uncultured and incredibly ignorant of the rest of the world. The advent of mass trans-Atlantic air travel combined with the Americanisation of our culture through TV and films has changed all that though. Whereas it used to be a real culture shock to meet Americans nowadays we just gawp at how how fat they are
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