Url redirection allows the browser to visit whatever url you pointed it to, however, the url displayed by the browser would be the redirected url.
For example, if foo.com redirects to bar.com/subdirectory, you would see bar.com/subdirectory in the browser.
With Addon domains, you will see foo.com in the browser since there is no redirection.
This is a simplified explanation of what the end user sees. For explanations of the backend (what the actual difference is), go Google it.