If I may:

Redshift: A PERCIEVED effect on the observed (visual or otherwise) emitted wavelengths emanating from a body that is moving away from the observer.

Blueshift: The same as Redshift except the observed body is moving TOWARD the observer.

The relative differences in body/observer velocities cause a percieved stretching/shrinking of the wavelengths themselves relative to the observer.

If the observer is moving on the same vector (direction/velocity) as the body, no shift is observed.

This is as opposed to the color of bodies based on their gravitational attraction. A neutron Star is dark red not because it's gravity causes a classic doppler redshift in it emissions, but because different wavelengths are affected differently by gravity itself. It is essentially the same principle as why the Sun appears redder when it rises and sets tho for a different reason.

By the time you get to the "density" of a Black Hole, ALL wavelengths have been bent back upon it, not redshifted or "sucked" into it.