Gyros and rotors both obey the same fundamental laws of physics that perfectly describe their behavior. F=MA applies equally to both. The differences lie in the forces that exist and where they get applied to the "disk". If you take a gyro with a mass and rotational inertia that is identical to a rotor, and apply the exact same forces to it that are applied to the rotor, then the gyro will demonstrate the exact same phase lag as the rotor.
There's nothing special about either a gyro or a rotor. They are both just a collection of interconnected masses moving in space. If you choose to define a gyro as something that must operate in a vacuum and have no forces acting on it other than gravity, then yes, a gyro is different than a rotor... but there is nothing in the physics that requires such a limited definition.