Beth,
You can find summaries from both Stalnaker's Compiled Military Service Records (CMSR) at the page on my 2nd Mississippi website below:
http://www.2ndmississippi.org/2nd_miss_part_1/CoL/CoL13.html
I suspect Adam joined the 2nd Mississippi Cavalry regiment and the official paperwork for the transfer never made it into channels, thus the reason for his reported status. This was not an uncommon occurrence. Unfortunately I have no information on place of burial for either man.
Hope this helps...
Mike Brasher