Definition: Red-Shift (RS)
Red-shift happens when the measured (observed) wavelength of a wave is longer than the wavelength of the wave when it was emitted. Inversely, a blue-shift happens when the measured wavelength of a wave is shorter than it was at the time it was emitted. Wavelength shifts can happen to all waves including sound and light.
the frequency of a wave is measured and the Observed Frequency (OF) of that
wave does not match the Emission Wavelength (EW) of the wave.
It is possible for the circumstances at the moment of emission to modify the wave in a way that the observer measures an OF different from the EW.
It is also possible for the circumstances at the moment of observation to cause the observer to measure an OF different from the EW.
Finally, the circumstances of the medium of the wave can modify the wavelength of the wave-in-motion during the Travel Time of the wave.
Whenever the OF does not match the EW, then a frequency shift has occurred.
If the OF is less that the EW, that is called “Blue Shift” because if a photon is emitted (EW) in the “yellow” wavelength but appears (is observed to be) “Blue” that means that something has happened to shift the observed frequency (OF) into a higher frequency (shorter calculated wavelength) than it was at the time of emission (EW).
A Red-Shift happens when the Observed Frequency (OF) of a wave corresponds to a wavelength longer than the Emission Wavelength (EW). In this case something has happened to shift the observed frequency (OF) into a lower frequency than it was at the time of emission (EW).
I will update when I find some good ones. A quick google search gave me garbage because any wave can be red shifted not just light.