In my lifetime, “parentheses” has been the canonical way to refer to () in the US. “Brackets” is an umbrella term that can describe one or all of (), {}, and [].

If you’re in a context where only one of the bracket types would normally be used, you can just call them “brackets.” Since many people never really use [] and {}, “brackets” casually refers to ().

To disambiguate, you can call () “open brackets”, [] “square brackets”, and {} “curly brackets.”

And for the cherry on top, {} can be called “curly braces.” That’s my preferred term for them. But it’s awkward to call [] “square braces” and () “open braces” :)

British English here: "(" is "open bracket" and ")" is "close bracket".

Together they are just brackets, not open brackets.

> Since many people never really use [] and {}, “brackets” casually refers to ().

I have never heard anyone call () "brackets". Is it more regional than just the US maybe?

Same. I've seen {} and [] both called braces and brackets, though usually in that respective order. The ambiguity is precisely why they are also called curly braces and square brackets. The double naming is more concrete.

I've never seen or heard any programmer call () brackets or braces. It's always parentheses. I may have heard a math or science teacher call them all brackets or braces, however, since they are synonymous there outside of odd exceptions like interval notation.

Fascinating! While I’ve definitely heard “brackets” used in the midwest occasionally, “parenthesis” is the standard term by far.

I've always called the curly ones brackets and the square ones braces.

No. Most US non-programmers call () parentheses, not brackets.