Ralph is saying that "the Canadian" River is not the "South" Canadian, though it is commonly called that along its entire course west of Eufaula and that was even on highway signs at bridge crossings in the past. The "main" river, with its source in New Mexico and its mouth below Webbers Falls is just "the Canadian River".
Before Lake Eufaula was built, the tributary of the Canadian from the mouth of Gaines Creek near Crowder to the Canadian just south of the town of Eufaula (where State Hwy 9A goes east from US 69) was the South Fork of the Canadian or "South Canadian". This stretch was sometimes known by the name of its tributary Gaines Creek. This is the part of Lake Eufaula Ralph is referring to that extends south toward McAlester and the same stretch that Larry is referring to from Crowder north.
It is confusing to me, especially in old documents, when the main Canadian is referred to as South Canadian. It makes it hard to distinguish between the main Canadian and the South Fork of the Canadian. When you see the term "South Canadian", you have to look for other clues to know if they are properly refering to the South Fork of the Canadian or if they are improperly referring to the main Canadian River.
The image below, with my labels added, comes from the 1955 State Highway map before Lake Eufaula was built.