Why A screwdriver antenna gets its name from the small DC gear motor (like one from a cordless screwdriver) that drives a threaded shaft, moving a coil in and out of contact with a sliding connection at the base. Changing how many turns of that base coil are in the circuit changes the loading inductance, which cancels the capacitive reactance of the short whip and brings the antenna to resonance on the chosen frequency. A short mobile whip is electrically much shorter than a quarter wave, so it looks capacitive, and adjustable base loading inductance is what makes one antenna cover many bands.
Watch out Extending and retracting the whip is how a telescoping or center-loaded adjustable whip is tuned, and a capacitance hat is a fixed top structure that raises the current distribution; neither is what the screwdriver motor is doing.
Screwdriver motor turns a screw that moves a COIL: motorized variable base inductance.