The Gillette Double Ring came first. The DR I have was manufactured in 1905 according to its serial number. My SR was made in 1911. It is postulated that the Single Ring came into existence because it was a bit easier to manufacture. I don't know if that is true or not. The razors appear to be almost identical except for the number of rings on the neck. They have the same head and screw mechanism. They each have the serial number on the barrel of the knob part.
My DR is in exceptionally good shape. The teeth are straight and there are no cracks in the handle. My SR is in very good shape, but the end teeth are bent a bit.
Update: June 14, 2017
For a comparison, I shaved with both DR and SR razors today. On the first pass I used the DR on the right side and the SR on the left. I used the same blade in each razor. On the second pass, I used the SR on the right and DR on the left. I noticed no measurable difference in the two razors. They are basically the same razor except for the rings.