Rewrites do not 'make' URLs. If you need a new URL, then use that new URL in the links in your pages.
It is links that 'define' URLs.
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If the internal filename on the server is not changing, theh use a rewrite as that will connect the URL request used out on the web, with the actual filename used inside the server, without revealing what that filename actually is.
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If you have a new URL to replace an old URL, then use a redirect to force requests for the old URL to make a new request for the new URL. However, you still need to use the new URL in the links in your pages, and no longer link to the old URLs.