Pressure
errors (i.e. errors in the measurement of pitot and
static pressure) are specific to the aircraft so we have to allow for them.
Instrument error is specific to the instrument so we have to get the instrument
calibrated and take it into account. Having corrected the indicated airspeed
for these two errors we have calibrated airspeed.
However small at take off speed we should correct for the effect of
compressibility and that will give us equivalent airspeed.
For a given weight and configuration the take off speed will depend on the
density of the air so we don't correct for that hence the aircraft will take
off at the same EAS.