There is one-and only one-species of cane native to the USA. Commonly it is called Cane or Switchcane (Arundinaria gigantea) depending on where in its geographical range you happen to be. This plant, a member of the grass family as is bamboo, ranges from Maryland/Virginia west to Missouri then South down into Texas then back east through the Southeast to central Florida. Several species of bamboo are in the USA, and all came from China. No where else. The Chinese Bamboo most commonly seen is Phyllostachys aurea.
Switchcane (that's what us Southern Boys call it) is the species that you read about in the Colonial Period ie "Cain-Tuck",etc. William Bartram talks about vast stands of it in present day Florida between Gainesville and St. Marks, the area where Daniel Boone and Squire were lost for several days in swamps.
So.....how do you tell native Switchcane from exotic Chinese Bamboo? Simple. Here's how.
Both are formed from hollow joints that have a hardened membrane seperating the joints in a very pronounced enlarged ring. If the next joint above the ring has an indention running up a short distance then the plant is exotic bamboo. If the joint is totally round above the ring, no indention just totally round, it is native Cane---the plant most likely used to make powder measurers. Hope this helps a little.