We have a copy of an 1820s Topographical Engineers map of the Indian Territory which shows the Canadian River, the North Fork (which also has a Deep fork), and the South Canadian -- which today is what comprises the arm of Lake Eufaula that extends to McAlester.

I have issues with those who mistakenly call the Canadian (proper) as the "South Canadian" as it forms the border of McClain and Cleveland Counties (e.g.) and elsewhere along its course west of Eufaula . . .

Ralph!