Questions on redshift 
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*What are different kinds of redshifts and are they related to each other? If yes, how?

*Is redshift a measure of distance or time or etc? For example when we say a supernova with a redshift of $z=0.9$ what exactly we mean?

 A: *

*There is only one type of redshift, but it may be caused by a couple different phenomena (doppler effect, gravity, etc.) Doppler redshift is caused by the emitter moving relative to the observer. Gravitational redshift is caused by time dilation in a gravity well, which alters the wavelength.

*Redshift is a measure of change in wavelength. z=0.9 means that the light wave we see is 1.9x as long as the wave that was emitted at the source.

A: There's essentially only one type of redshift - the special-relativistic Doppler shift, properly adapted to the rules of general relativity. In curved space-time, there's no global notion of relative velocities, and we need to parallel transport the emitter's velocity vector to the observer along the light path.
In addition to this abstract notion of redshift, in special circumstances, there do exist more tangible interpretations.
In particular, there's gravitational redshift (loss of energy when climbing out of a gravity well) and cosmological redshift (increase in wavelength due to Hubble expansion).
The cosmological redshift can be used as both a measure of distance and time (the light of galaxies we observe right now was emitted both far away and a long time ago) after calibration against the expansion rate.
