All of the Southern and CofG "brick" cars need a detailed article in TIES as they have quite a history.
A "short" answer to your question.....working backwards....
The Southern 505700-505848 double plug door 40' box cars were renumbered from CofG 47 and 4800 series cars in May and June, 1976 (most CG cars were renumbered and re-stenciled Southern at that same time. I've attached a nice Oscar Kimsey photo of Sou 505703 taken at Nixon, GA in 1973 and Sou 32161.)
When they were rebuilt from standard 40' box cars to CofG brick cars is a bit more complicated. The first version of Southern/CofG cars for brick service were done "on the cheep". They had double sliding doors and cushion underframes but the underframes were not modified to deal with the width of the double doors. Typically door side posts connect to the side sill at a crossmember to carry the load from the door sills to the underframe. Because the rebuilt door sills were at a different location, their load was transferred to only side sill then the side sill carried the load to a crossmember. The problem was the vertical load at both the bottom of the door sill and at the crossmembers caused cracks in the side sills. Note the reinforcements on the side sill below the door sill on Sou 32151 to try to correct the problem. (I'm sure a mechanical engineer could provide a better explanation.)
As some portion (?) of the sliding door cars were rebuilt to plug door cars, their underframes were modified to correct that problem. The plug doors helped carry the load across the door opening to the door sills.
The idea was that the CG brick cars were to be rebuilt from CG box cars to keep the accounts straight bt I don't believe that was always the case. During the rebuild programs of the 1960s, if a CofG car was not available, a Southern car would be swapped in the accounts and a Central car used for a Southern rebuild. I expect we can dig into the SCP files in the archives to show all/most of the brick car renumberings but that take someone to help with the research.