Speed doesnt have an effect on the altitude reading of an Altimeter, how ever altitude can have an effect on speed indication. At a higher altitude there is less "ambient " pressure on , so the pressure due to speed in the pitot probe will be less. This difference is compensated for by mixing in the static air pressure. Speed doesnt affect static pressure, so doesn't alter altitude readings.
An altimeter when calibrated in a lab is set to read a certain calculated standard height for a certain pressure. eg 10000ft = 1013mBar or hecta whosits.
The air pressure over an area changes, so if flying straight and level, over perfectly flat terrain, its possible that an altimeter that has been set at a reference pressure (or even zero feet at the departure point) will show ( and record) a change in height. In this instance ( hypothetical of course) the RAD alt which uses radar waves to measure its true height above the ground (and record it). On examination of the recorded data it would show a difference between the two readings.
Its not a question of accuracy of the calibration of either device , as they are measuring differnt things. the altimeter measures air pressure, and the radalt measures the time it takes for a radar pulse to return to it.
Note, that a radalt is only accurate when aimed vertically at the ground, any tilt in the aircraft axis will give an erroneous reading.