Pat, I have both species of native cane you have described in my part of the state.The type I think of as switch cane has very thick walls as you have said, but the diameter is somewhat on the small side and is more apt to have dog leg nodes with flattened internodes. But it makes for a very good, strong arrow shafts if you are selective with what you cut. By the same token, I don't waste my time with the giant river cane with the thin walls. Makes a good fishing pole but not my preference for arrows.
With that being said, the type I call river cane and prefer has some of the characteristics of both switch cane and the giant cane. It grows taller than the typical switch cane, reaching heights of 9' or better with good wall thickness and diameter. Much of what I cut grows as individual plants scattered under old timber in creek bottoms. Typically, it has a small diameter in proportion to its height with a very gradual taper. I have a piece in my workshop that is almost 8' long that is 3/8" at the butt and 11/32" at the top. I will try to take some pictures tonight or tomorrow if the rain holds off and post them.