M813 = non dropside bed
M813A1 = dropside bed
The analogous G744/M39 truck is the M54A2 and M54A2C. It doesn't have to be an A2, the "C" is the important part.
I think I've seen photos of M813s and M54s with an additional toolbox above the fuel tank under the bed. It seems like this is a non dropside thing only.
The confusing part of this is that the deuces and G744/M39 trucks use the "A" numbers/revisions to designate a powerplant change, the M809 trucks never had a powerplant change and have different "A" numbers to designate different body styles. The M820 is the only other M809 that has a different A number to my knowledge.
Oddly enough, while the dropside deuce (M35A2C) is rarer vs the regular M35A2, it seems like the non dropside (M813) 5 ton is the rarer 5 ton cargo.
Hopefully all this makes sense.