FYI there is a Mississippi Confederate Grave Registry on line at http://mscgr.homestead.com/MSCGRchar.html.
I looked briefly, and I found, only one Clark in the 38th Miss.. He is listed as being in the 38th Inf. (Mtd.)
Could he be related to A.D. ?? Enlistment date is shown as April 26, 1862.
In some instances you can go by enlistment dates and unit identification, to help find some relationship.
In this case having been in the same unit, and both were in the same hospital, could be a big help.
Georgia has a fantastic on line database http://www.csagraves.com/index.php
Other states that have on line Confederate grave information are: Alabama, Arizona, Louisiana,
Maryland, and Missouri. And the SCV has one.
Go to the Georgia site and scroll down on the home page, there is a list of all the databases, click
on any one to go to that database.