For definition of exception, head to google.
In regex, you simply match input for a given pattern without worrying for exceptions. Using parseInt or parseLong, you actually try to parse given string input to number (needed when you need given string input as a number in your application, since external inputs are always as String) and in case of error, gives exception that you should handle.
In regex, you just match the input against a pattern without the worry of exceptions, since you are not actually parsing it to number.
For example, head to http://regexr.com/3dmdj
and mouseover the pattern.