According to the Singer catalogues from the early 1900s (
http://www.sil.si.edu/DigitalCollect...es/image11.htm and
http://www.sil.si.edu/DigitalCollect...ges/image3.htm ), the first number is the Class of machine and the number after the hyphen would be the variety. In the case of those machines manufactured at Kilbowie the variety is listed after the "K". I have also read that the first number is the model, and the sub-model is listed after the hyphen or K.
In addition to what has been mentioned, I think that the 66-1 and 66-3 are back/rear clamp presser foot. I think that the 66-18 is godzilla finished but otherwise the same as 66-16 machine. I have the 66-16 and it is the glossy black finish. Another source to find some of the differences between the varieties or sub-models can be found at
http://www.ismacs.net/singer_sewing_...sses-1-99.html
Janey - Neat people never make the exciting discoveries I do.