River cane(A.gigantia) is the largest of the native canes. It grows to over 15' tall. It also has larger culms, up to 3/4" in diameter with thinner walls and a large center hole. It also has a more pronounced sulcus, the indentation above the node bud. The nodes are also larger in diameter.
Switch cane only grows to 6' to 7' tall and hill cane is similar.
There are many exotic canes(bamboos) growing all across the US. Most were planted in the early 1900s for erosion control and wind breaks. They range from about 1/4" in diameter to 6" or more.
If you live in a warmer area, hardiness zone 8 or higher, Bambusa multiplex is an excellent arrow cane. It is a clumping type bamboo growing in a 8' to 10' diameter clump and not spreading farther. The culms grow to about 15' tall and maybe to 3/4" in diameter. The culms are round with little to no sulcus and internodes 12" to 15" long so you only have 2 nodes to each arrow. This bamboo has a small center hole with quite thick walls. It will not grow in colder climates...or I'd grow it.