Er, haven't those definitions been out of date for at least a decade, if not 3?

If an office policy is semi formal, do people turn up in a black tie?

Why are black tie parties "black tie" parties and not "semi formal" parties?

IMO you've listed "opera" followed by "black tie."

"Formal" would be "a tie and jacket," "semi formal" would be a jacket without a tie, or (shudder) a tie without a jacket, and then business casual is where the polos come in.