Hi Casey,
I go into many items in my book "Civil Engineering for Outdoor Railroads Volume 1". It was written for the hobbyist in mind. Three pages are used to discuss a "Degree of Curvature" and the highway (arc) definition and the railroad (chord) definition.
The degree of curvature was used for laying out centerlines (originally for railroads but eventually also streets roads and highways). It is/was an easy way for field crews to lay out a centerline before the advent of computerized Total Station machines.
This has been discussed on this board many times in the past so I will not take up more web space.
However, if you would like to read the three pages in my book discussing how it came to be, how it is defined, how the two definitions correspond and so forth; I have placed the copyrighted material on my web site. It is 640K long so it might be a while downloading if you have a dial-up connection. If you wish to distribute this excerpt from my book, feel free to do so as long as it is not for commercial purposes.
If you have specific questions, I'll be glad to try to answer them.
Doug