The one on the left looks like a shaft straightener. The Native Americans would run this over the shaft of the arrow to eliminate any irregular points or contours. I used to find similar things in Nebraska, most of which were Pawnee, and Sioux. Not sure if that's what it is, but that's my best guess.
I kinda agree with you on that with the circular hole in the center. They must have used something with it for leverage. That or it could have been used to shave the bark and branches off of the arrows with the sharp edge it has.