And then there is the definition of a road. Walking on a forest service road and shoot a grouse? Guess that is up to the warden too?
The term is "public highway", not road. It includes essentially all roads, streets, highways and other driveable surfaces open to the public. 
It has been explained to me "public highway" is as you said,
"essentially all roads, streets, highways and other driveable surfaces open to the public" with an addition of... if it is maintained by public funds i.e. tax dollars it is classified as a "public highway."