@Setanta,
Setanta wrote:Perhaps Centrox could comment on the terminology used in England.)
"Brackets" is the general term for this family of symbols, and particular ones are qualified by a preceding word such as round, square, curly, angle, etc. We are aware that Americans may use this term specifically for square brackets.
Round Brackets
() are also called parentheses, especially in American English.
Square Brackets
[] are also called brackets, especially in American English.
Curly brackets
{} are also called braces, especially in American English.
I would add that where it matters, careful British writers use the same terminology as Americans - I mean people involved in preparing material for printing, mathematicians, computer programmers (these symbols are used in many computer languages and have an exact meaning).
Ordinary people tend to call parentheses just "brackets", and when (say) dictating text, might say "open brackets" and later "close brackets". Square brackets are a bit specialised in ordinary text.