Hubble's law originally mentions the speed (i.e. proper motion) of a receding galaxy, as calculated via the Doppler effect from the observed redshift. However, the observed redshift is today explained as being due to the expansion of the universe (and thus not related to the Doppler effect).
What is the modern way of interpreting Hubble's law? I mean, if the galaxies have no proper motion? Then, is it still valid to use the Doppler effect ($v=zc$) to calculate a velocity? What does "velocity" in Hubble's law mean, and how is it related to the observed redshift?
Most of the information on the Internet seems to be self-contradicting and/or inaccurate.