I think you have misunderstood the terms "redirect" and "rewrite".
With a redirect the browser asks for a particular URL and the server replies with a 301 or 302 status code and suggests the browser asks for a different URL. The browser automatically asks for that new URL and the URL shown in the browser address bar changes to show that new URL.
With a rewrite, the browser asks for a particular URL and the mod_rewrite rules change the internal file pointer so that Apache fetches content from a different place on the hard drive than might have originally been expected.
[edited by: phranque at 12:23 am (utc) on Oct 26, 2013]
[edit reason] fixed typo [/edit]