It is not difficult to understand the differences between 'Doppler redshift' and 'Cosmological redshift' conceptually. But how do astronomers distinguish them when doing observations?
[Physics] ‘Doppler redshift’ Vs ‘Cosmological redshift’
cosmologydoppler effectgravitational-redshiftredshift
Best Answer
I think there are duplicates of this, but couldn't immediately locate them.
The answer is you cannot tell observationally whether a single redshift measurement is caused by the expansion of the universe or by something moving away rapidly.
However, if one wished to interpret the ensemble of redshifts that we see in a non-expanding universe, then you must place us at the centre of the universe. You would then have to explain why more distant galaxies are moving faster and why at very large distances, the simple Hubble law breaks down (and the microwave background and the primordial elemental abundances and so on).