If you unscrew something such as a sign or mirror which is fastened to something by screws, you remove it by taking out the screws. He unscrewed the back of the telephone and started connecting it to the cable
If you unscrew something such as a lid, or if it unscrews, you keep turning it until you can remove it. She unscrewed the cap of her water bottle and gave him a drink The base of the lamp unscrews for wiring and mounting