In this paper, we clarify the difference between the Hubble expansion and the Doppler shift
pedagogically and illustrate both physically and mathematically why the Hubble expansion cannot be
regarded as a velocity. Therefore, we suggest to replace the misleading word ‘recession velocity’ to
be ‘ Hubble recession ’ to describe the cosmic expansion. We further derive how the peculiar
velocity of a galaxy is related to its observed redshift and proper distance, which has practical
use in the galaxy redshift and distance surveys.