Ai actually find it disterbing when people lable any old stick that they happen to pick up as a “hunting stick” or “rabbit stick”. You could just as easily, and just as erroneously, call the stick a “prayer stick” or a “majick wand” or a “fire drill”. A stick picked up from the ground is just a stick, no matter what you want to call it, unless it is properly prepared for a specific perpose.
Hunting sticks are ALLWAYS flattened in some way, usually by carving. To what degree and specific shape differs from place to place. Australians produce many kinds, some like a propeller blade, in order to change course in flight (for various reasons, among them was to return if it didnt hit the target). In the southwest region of North america, most were flattened and given a crescent or overly wide “V” shape, while some in Baja California were made into a wide hook (1 1/4 feet diameter) and others, into a “?” shape (handled and thrown with the inside of the curve facing forwards, for the reason that this gave more power in the spin). For exact proportions and step by step construction of California rabbit sticks, see my alltime favorite book “Survival Skills of Native California” by Paul D. Campbell.
Also, such implements have been used (atleast in California) to hunt deer (thrown at legs or, if in a good posision, vertically thrown at neck) and some limited capacity in war (usually thrown just before close range weapons were imployed).