In "Remembering V.M. Slipher’s work at Lowell" (April 2020 - https://www.astronomy.com/science/remembering-v-m-sliphers-work-at-lowell/), Astronomy magazine's editor David J. Eicher writes that redshift indicates the velocity of recession, and also says USA astronomers Vesto Melvin (known as V. M.) Slipher and Edwin Hubble * discovered the expanding universe. My opinion is that the Editor is right to give V. M. Slipher credit for a major cosmic accomplishment but mistaken about the nature of that accomplishment. I also think Slipher and Hubble didn't discover the expanding universe because redshifted spectral lines don't indicate recession of astronomical bodies. Rather, Slipher found the first proof of Albert Einstein's General Relativity Theory - beating Arthur Eddington's 1919 eclipse measurements, and even beating the full General Relativity theory's 1915 publication by at least a year.
* Edwin Hubble (1889-1953), the astronomer credited with discovering cosmic expansion, remained doubtful about the expansion interpretation for his entire life. He believed “expanding models are a forced interpretation of the observational results.” (E. Hubble, “Effects of Red Shifts on the Distribution of Nebulae”, Ap. J., 84, 517 [1936]) According to astronomer Allan Sandage, "Hubble believed that his count data gave a more reasonable result concerning spatial curvature if the redshift correction was made assuming no recession. To the very end of his writings he maintained this position, favouring (or at the very least keeping open) the model where no true expansion exists, and therefore that the redshift "represents a hitherto unrecognized principle of nature." (Sandage, Allan, "Edwin Hubble 1889–1953", The Journal of the Royal Astronomical Society of Canada, Vol. 83, No.6 [1989])
V. M. found evidence of Relativity's gravitational redshift, which was found by Einstein 8 years before his full theory. The term "gravitational redshift" refers to the shift of wavelength of a photon to longer wavelength (the red side in an optical spectrum) when electromagnetic waves radiate within a gravity field. Relativity says gravity results from the curvature of space-time. Therefore gravity is spacetime - and the more spacetime there is between Earth and a star or galaxy, the greater is the gravitational redshift. The redshift has nothing to do with velocity but increases with distance. We should not be surprised that light waves do not follow exactly the same Doppler effect as sound waves, since they have a different form. Light and other electromagnetic waves are transverse while sound waves are called compressional or longitudinal. Andromeda galaxy's apparent approach is related to Slipher's finding that "spiral nebulae" (as galaxies were called 110 years ago) are rotating. A large, close galaxy like M31 (Andromeda) would appear to be approaching us because it isn't far enough away to send us light that's significantly redshifted; but a huge number of its stars are currently approaching us as they orbit Andromeda's centre, and therefore sending us blueshifted light.