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I heard somewhere that the odometer reads only the rotations of the axle, so changing differentials would not affect it. However, that would mean changing tire size would. Is this concept the same for the speedometer?
The speedo and odometer usually get their signals from the same place.
Most carbed vehicles take the readings off the tailshaft of the tranny or the transfer case. So changing tires and rearend gears will change the calibration.
The pickup is on the axle on those, so tranny or rear-gear changes don't affect the accuracy of them, but tire size changes will. There is however, an adjustment procedure (I've seen it on this site, but don't remember where - do a search) that will let you re-calibrate the speedo right from the dash. It uses the pushbuttons for the trip odometer and reset.