Our 3D maps of galaxy distribution are actually maps of direction and redshift. We assume that distance is proportional to redshift and that the redshift is entirely due to Doppler effect. Those assumptions allow us to translate redshift to distance. The maps also assume that the objects are stationary relative to the

comoving space around them, since we have no way to detect whether they are or not. We can detect radial motion of nearby galaxies, so we know they do move; but that relative motion is tiny compared to the expansion of space between us and the more distant galaxies.

There are several kinds of distance in cosmology. The most commonly used is light travel distance, which is the amount of time we believe it took for the light to get here, assuming that the space expanded at a constant rate that whole time. The recent discovery that the expansion seems to be accelerating results in a slight alteration of our estimate of how long light of a given redshift took the light to get here. That alteration is included in the most recent 3D maps.

So in most cases, we are looking at maps of light travel distance, which gives us a pretty good idea where the galaxies were when they emitted the light we see. That does not tell us how far away the objects are now. That is called luminosity distance; it is based on the fact that light intensity diminishes as the inverse square of distance. However, the assumption that the distance now is the luminosity distance is based on assumptions that the object has not moved significantly in relation to the comoving space around it and that the space has continued to expand at the same rate everywhere for the entire time it took the light to get here. These are assumptions that most cosmologists take for granted, though there is no possible way to prove them correct.