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The principles of horizontal deflection and vertical are different.
For horizontal deflection, the ideal is a pure inductance in which current increases linearly over time due to a constant drive voltage. In reality, there are resistive losses that have to be overcome, but the drive is still applied by hard-switching a voltage supply onto the yoke and then diode conduction (by the damper) of the current in the other half of the sweep. Tube and transistor circuits differ in that tube circuits generally are higher impedance (higher voltage and lower current) than transistors.
For vertical deflection, the operation is much more of a linear amplifier arrangement, although there is enough inductance to cause a pulse voltage on retrace. By the way, this makes it possible to use feedback techniques to make the current perfectly linear and eliminate a manual vertical linearity adjustment (which I recall was done in some Zenith designs).
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