Servo electronics are designed to cause the servo to hunt for a new position at the slightest stick movement, then come to a stop and stay there on arrival. They are also designed to start slow and slow down as they approach their new position which generally prevents jitter. When used as a motor control, this gives a very finicky stop position. A slowly creeping prop is rarely a problem. A creeping winch or steering could be a problem.
A purpose designed ESC (using the same chip but with a couple of different peripheral components in pre-PIC days) has a wider deadband just so that neutral can be found consistently. Effectively when the stick is moved, both are driving a motor to a new position. A servo "knows" when it has got there and stops, an ESC or modified servo never "knows", so keeps going until the stick returns to neutral. A winch servo has an extra bit of gearbox between the output shaft and the position sensing pot to give the extra travel while not driving the pot wiper through its end stops.
Servo electronics do rely on having a very stable voltage supply to prevent creeping if used as a speed control, of interactive buzzing if used as a servo.