Ilene Strizver, founder of The Type Studio, explains the differences between parentheses, braces and brackets at Fontology.

The character set of a typeface includes a broad range of punctuation marks. Among them are parentheses, braces and brackets. These three pairs of symbols all serve to enclose additional information – words, numbers or symbols – generally not essential to the meaning of the sentence or paragraph. Although all three marks share this function, they have specialized usages as well.

Via Fonts.com