(Automatic Control) Why is the proportional regulator differential?

From the step response curve of the proportional regulation law, it can be seen that the static deviation of the regulated quantity still exists after the regulation process, because the output control function of the proportional regulator is proportional to the input deviation signal. If the deviation of the regulated quantity is zero after the regulation process, the control signal output by the regulation is required to be zero, that is, the control function is zero, so the existence of interference signals will not stabilize the system, so the deviation of the regulated quantity still exists after the regulation process. When the adjustment process ends and the deviation of the adjusted quantity still exists, it is called differential adjustment. Obviously, the law of pure proportional regulation is differential regulation.