Looking at the images of the 6 types of rail, I am familiar (not an expert) on 5 of the 6 types shows, plus at least one other not shown: strap rail. That was essentially just a piece of iron flat bar, which varied in thickness and width according to the specific needs of the railroad. Those tended to deteriorate more rapidly than the others because they were placed on wood and spiked down to wood stringers longitudinally and the which was not treated deteriorated rapidly plus did not withstand increasing weights of equipment at in got larger and larger.
I know many southern railroads used it, but can't address which or when or for how long, including those in and around Atlanta. The well-known Richmond & Danville RR definitely used it and its deterioration were what caused the slow flight from Richmond by the fleeing Confederate government in April 1865.
All that said, that other thing in the photo (the sort of "P" shaped segment) is a big mystery to me. I can't picture how it was secured to the ties and suspect it was not long in use or was in use in conjunction with another similar piece of iron. I have never seen that before and will do some research exploring sources around here. I don't think I have even seen it in places like the drawings you have either and that, to me, makes its use as rail somewhat suspect since those drawings are pretty good depictions.
My 2 cents worth, not much, but I tried.