NO. A controlled substance or a scheduled substance is one that is listed in the Controlled Substances Act. It has five (5) classifications or schedules.

Some controlled substances are always illegal such as cocaine. Xanax is a controlled substance but it requires a prescription to purchase AND possess.

A RX drug is one that the FDA requires a prescription to dispense. You can possess them without a prescription as there is no penalty. Since the drugstores cannot legally SELL them without a prescription you cannot legally BUY them without a prescription but, again, there is no penalty for possessing a non-controlled but nonetheless PRESCRIPTION drug.

Again, state laws vary.