The "store" configure.php
This contains settings for the pages the general public can see. It is also refereed to by other names such as the "storefront" or "CATALOG" side of the store.

The "admin" configure.php
This contains settings for both the administrative side of the store and also the catalog side of the store.


So yes it is best to use the same settings in both places for corresponding entries. For example: 'HTTP_CATALOG_SERVER' in the "admin" configure.php should be the same as 'HTTP_SERVER' in the "store" configure.php.

You can read more about the configure.php and keep in mind most entries with 'CATALOG' in the "admin" configure.php are for the "storefront" (some parts of the "admin" such the define editor needs to know where the CATALOG files are located).