So my understanding is that F&AM were chartered by the Moderns and AF&AM were chartered by the Ancients and their ritual derived respectively. Granted the Moderns and Ancients had pretty similar ritual to begin with given that they were one body prior to the split. This would be the cause of a similar yet different ritual, correct?
My understanding of South Carolina's different AFM is thus: The Moderns chartered a lodge in SC, the Ancients chartered a lodge a year later. A merger was done and a compromise in the name was chosen, Ancient Free Masons
As for DC, I've never heard of a good reason for the difference other than they just picked it so as to be different. I'm sure there's a better explanation, but I've yet to find it in any histories of the GLoDC.