When the use of LaTeX or MathJax or other typesetting system is not an option, one can still type the braket notation $\left<\psi\right|$ and $\left|\psi\right>$. The simplest way is probably to use the plain "less than" and "greater than" characters found on a typical North American keyboard. However, the results often don't look quite right (to my eyes). One could instead use Unicode characters, such as the "mathematical left angle bracket" (U+27E8,
⟨) and "mathematical right angle bracket" (U+27E9,
⟩) but there are others, such as the "left-pointing angle bracket" (U+2329,
〈) and "right-pointing angle bracket" (U+232A,
〉). (C.f. an answer to a different question in Stack Overflow.) There may be differences in the semantics of these characters that I don't understand, and may have implications for accessibility (e.g., for screen readers).
Are there principled reasons for using a specific set of characters for the angle brackets in braket notation?