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” :)
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” :)