Red shift and red light are two different things. Red/Infra-red light is simply light lying in the well-known frequency range whereas red-shift is an illusion which is a consequence of Doppler effect, which alters the original frequency as a consequence of high relative velocity between source and observer.(Doppler effect is applicable for sound as well. ) Now, coming to the part where we distinguish the two - it is a known fact that stars are mostly made up of elements hydrogen and helium. When we compare the emission signature from these stars and compare it to standard spectroscopic signatures, we notice a regular shift in the entire spectrum. That's how we know that the stars are moving away. Stars that are truly red show also show this shift towards the infra-spectrum when compared with the standard results. I hope this answers your question. :-)