To me, if one would need to correlate the output voltage to a speed, it would make more sense that that speed would be the speed of the stylus relative to the cartridge itself (*vertical* movement) as that's the movement that induces the voltage to begin with.
Yes, the output voltage is a function of the velocity with which stylus deflection occurs, relative to the cartridge body, the deflection being lateral for the mono component of the signal, and vertical for the stereo component of the signal.
However, for a given physical excursion of the groove, laterally or vertically, the speed of that stylus deflection relative to the cartridge body will vary depending on the tangential velocity of the groove, which gets smaller towards the inner part of the record. Therefore for a given music signal the physical distance over which that excursion occurs has to be smaller at the inner part of the record compared to the outer part of the record, in order to result in the same stylus deflection speed. Tony put it well: "The musical information is essentially packed tighter at the inner grooves of the record because the linear velocity is lower."
Regards,
-- Al