Difference between error calls?

What's the practical difference between using either:

if (condition) {
   throw new Exception(language::translate('error_email_address_missmatch', 'The email addresses do not match'));
}

or

if (condition) {
   notices::add('errors', language::translate('error_email_address_missmatch', 'The email addresses do not match'));
   header('Location: '. document::ilink());
   exit;
}

to catch errors?

Exceptions can be caught. And I use them primarily for not having to do your second example multiple times.

https://www.php.net/manual/en/language.exceptions.php

Sometimes when I throw an Exception, it doesn't produce the text in a red banner. Instead it prints the raw error code on a blank page and I can't figure out why. Any ideas as to what to look for?

So, you use catch to make your own handler of the exception. If an exception is not caught, it ends up in PHP's error handler.

My mistake. I didn't place the exception inside the try{} block so, of course, it wasn't caught. 😣