Google J&S Hawken Rifles. Look at the rifles offered by Don Stith, WEB Selb, and the Hawken shop.
You will see as Zonie stated, iron mounted, walnut stocked plain rifles. The Plains versions have a barrel that tapers from about 1 1/8" across the flats to just under 1" at the muzzle. Caliber will be in the 52 to 56 caliber range.
The Traditions rifles will be brass mounted, plain maple or hardwood stocks and a straight barrel of 50 caliber with some 45 and a very few 54 caliber versions. To be fair to Traditions, their rifles look like the rifles that the Hawken brothers built for the local trade or rifles that Dimmick built for the local Missouri deer hunting sport.
A J&S Hawken built for the plains is very different from the rifle offered by Traditions.