the motor is (mostly) the combination of the voice coil, the magnet and the steel. when current is applied, those are the parts that make the cone move.
iirc, the ho has more windings on the voice coil, which allows it to take more power, but increases inductance, which increases several forms of distortion. how much difference you will be able to hear is up to you.
the hf has a softer suspension, which is better for detail. the ho has a tighter suspension which is better for pounding on the driver, particularly in ported applications with no high pass filter.