It's so cute the way you call them brackets. Here they're parenthesis of they're curved, ( and ) and brackets if they're angular [ these ] and < these >.
Also brackets are used to hold up shelves.
Brackets: ( )
Square brackets: [ ]
Curly brackets (at least that's what my Maths C class decided to call them): { }
And I only associate < > with greater/less than, and diamond. Even though it's not a diamond. I certainly don't associate them with brackets.