Red shift and blue shift are exactly the same thing. If you think about light as a wave, like sound, approaching objects have scrunched up waves (blueshifted light) and fleeing objects have spaced out waves (redshifted light). The exact same reason a car horn has higher pitch when it is approaching you and lower pitch when it travels away. The intensity of the effect is correlated to the speed limit of the medium so since light is so fast this effect is typically very small.