I wrestled with this too. WP does not like using both of those fields. Pick one or the other. For a subdomain to work, you need to pick the other, which means customizing your subdomain.
The simplest way is to set up your subdomain so that it points to your uploads folder (wp-content/uploads by default)
In this case it would be:
Store uploads in this folder: (blank)
Full URL path to files: http://media.mywebsite.com
And your subdomain, media.mywebsite.com needs to point to the wp-content/uploads location.
A more complex system is described here:
This lets you change the default folder from wp-content/uploads to anything else, like media. However, this folder must be within your wp directories.
If you have wordpress installed into the root, you could point this to your subdomain. But if you installed in something like wordpress/, you'd need to create wordpress/media, set that as default as described in the link. For your site that would be:
define( 'UPLOADS', ''.'media' );
I'm not able to get this method to reliably work with my subdomain, though. There's probably something additional needed to the config to get it to change the upload directory and use another url, but I don't know what it is.