> With bugs, of course, being mistakes around "business" rules, and exceptions being mistakes made around computing environment rules.

For me, bugs are all mistakes which manifest themselves in software misbehaving. Maybe it surfaces by a program crash of an uncaught exception or an error message presented to the user, a program termination, a wrong result, ...

> How do you combine a programmer making a mistake with exception handlers?

I write a bug leading to an exception sometimes and catch the exception, then try the operation again, or show an error to the user

> For me, bugs are all mistakes which manifest themselves in software misbehaving.

And that's fine. It is not like there is some magical deity in the sky that creates and enforces the law of language. Words are just made up by humans on a whim. If I want to exert my own whim and call that "zigglefritz" instead, that works too.