In my experience at least, HGV driver
isn't used in the US, though it could be a recent import I'm not aware of. So it and lorry driver
are probably only BE. (Or possibly related regions; it might be helpful to check AusE, CanE, Africa, etc. specifically.)
AE is primarily truck driver,
and yes, colloquially also trucker
, so there may actually not be any overlap.
As far as I know, Teamster
isn't actually used in this sense in AE except as a proper noun (i.e., capitalized), where it now means a member of the Teamsters labor union, a large traditional union in North America whose members include some truck drivers, but also many other blue-collar workers. But the labor movement has become so depleted in the 21st century that most truck drivers now probably don't even belong to a union, sadly.https://en.wikipedia.org/wiki/International_B...
There are several other words in AE for the large truck that long-distance drivers drive, probably covered in several other threads in the forum archive (Suche in allen Foren, above left): semi, 18-wheeler, tractor-trailer,
For highway signs requiring heavy trucks, dangerous loads, etc., to take alternate routes, I think AE just has something like 'heavy vehicles' or a weight limit in thousands of pounds, but that may well be regulated at the state level. Extra-long loads, like trailers carrying long pipes or steel beams, and extra-wide ones like mobile homes being moved, typically have to have escort vehicles front and back with flashing lights, and a sign saying 'Oversize load,' at least in my state.
See what other AE speakers say.