It may seem to be a muddle, but there is a very real difference to a game warden if you are fishing "flies only" water in many states. According to my guide, you can fish flies from a spinning rod in the "flies only" water on the North Branch of the AuSable River legally. (He told me several years ago.) The same cannot be said by fishing non-flies with a fly rod.
In many places, molded jigs are specifically excluded from the list of what is considered to be a fly, but bead-head flies are allowed. Working around fine lines should not trouble people who tie flies or use fine tippet material.
Ed