Cleaning rods often come made of light weight aluminum, and are in sections for easy transport. Range rods are usually solid pieces of steel, brass, ( can be hollow brass tubing in some makes) and Aircraft Aluminum alloys. They are one piece units, and that is why they are usually always referred to as Range Rods. They are not very easy to transport with a gun into the field while hunting.
Ramrods are almost always made of wood, or some kind of synthetic fiber, and are made to be carried with the gun.
In reality, a range rod can be used for all the purposes.
I have a hickory Ramrod, that I put a large "doorknob" handle on that I turned on a lathe from a piece of walnut, and it goes into the field and to the range with me to load and clean my 12 ga. DB shotgun. The handle is stout enough and the rod sturdy enough to allow me to use it to pull patches, and even round ball, should I ever try shooting them out of my shotgun. Because of the size and weight of the handle, I carry it down the middle of my back, the shoulder strap of my hunting bag holding it to my back, and the jag stuck under my belt. The knob sticks up over my hat, behind my had and does not interfere with any movement when shooting. I removed the pipes from the underside of my barrels, and carry no stick with the shotgun itself.