The observed speed of light is indeed the same for all observers, regardless of their relative velocities. This principle is a fundamental concept in physics and is known as the constancy of the speed of light. It is a cornerstone of Albert Einstein's theory of special relativity.
However, this constancy of the speed of light refers to the speed of light in a vacuum (approximately 299,792,458 meters per second). When light travels through a medium like air, water, or a transparent object, its speed can be slower than the speed of light in a vacuum due to interactions with the medium's atoms and molecules.
Redshift, on the other hand, is not related to the speed of light but to the wavelength of light. When an object is moving away from an observer, the light it emits gets stretched, causing an increase in its wavelength. This phenomenon is known as redshift because, for visible light, longer wavelengths are associated with the color red. The faster the object is receding, the greater the redshift.
Redshift is a crucial phenomenon in cosmology and has been instrumental in understanding the expansion of the universe. Edwin Hubble's observation of redshift in distant galaxies in the 1920s provided strong evidence for the expansion of the universe. As galaxies move away from each other, the light they emit becomes redshifted, and this effect increases with their increasing distance from us.
So, while the constancy of the speed of light holds true, redshift is a consequence of the expansion of the universe and is not related to the speed of light itself.