The history of these terms is different from what people may think. Railroads had approved watches for use. At first these were lists of specific watches, and later they became lists of features and characteristics a watch must have. Each railroad had it's own standards, and they changed over the years. Information on what was approved does not survive to this day for all railroads.
The Lake Shore and Michigan Southern Railroad called on Webb C. Ball, a Cleveland jeweler, to investigate time keeping issues on the rail lines. Ball was tasked to establish standards for railroad watches and create regular inspection system with careful record keeping for each individual timepiece in use on the railroad.
As an aside, my Grandfather briefly worked as a railroad watch inspector. As another aside, this is how the expression "on the ball" came into use, as a way of saying "on correct time."
Anyway, once these standards were created, watch manufacturers began designing watches specifically for railroad use. Watch manufacturers also figured out quickly that the public was aware of all this and that associating their product with railroading sold more watches. They put pictures of steam engines on dials and cases, used railroad style markings and hands, and started talking about "railroad grade". But this claim didn't necessarily have anything to do with whether or not a specific railroad had approved a given watch that given year. As today when a pickup truck is labeled by a car maker "heavy duty", the term can be arbitrary.
Here is one specific list. In 1890, at a watch inspectors convention it was determined that watches for use on railroads be adjusted to five positions and temperature, have a double roller, be lever set, wind at 12 and have a plain Arabic dial. 12 size were not acceptable. The following watches were agreed upon.
Waltham's Vangard 23 jewel, Crescent St., 21 jewel and Riverside, 19 jewel.
Elgin's Veritas, 23 jewel, Father Time, 21 jewel, and B. W. Raymod, 19 jewel.
Hamiton's No 950, 23 jewel, No. 992, 21 jewel and No. 996, 19 jewel.
Illinios's Sangamo Special 23 jewel, Bunn Special 21 jewel and Bunn 19 jewel.
Hampden's Special Railway 23 jewel, New Railway 21 jewel and Railway 19 jewel.
South Bend's Special Railway 21 jewel, No. 227.
Haward's 23 jewel, 21 jewel and 19 jewel.
Ball Official Railroad Standard 23 jewel, Standard 21 jewel and Standard 19 jewel.