Sure thing, Gnargenox!
I want to explain a little further with the galaxy motion, since I was in a rush earlier, that there are really two motions to think about. One is their physical motion through space (the "peculiar velocity, which is usually a few hundred km/s with respect to the cluster center), and the other is the "recession velocity" due to cosmic expansion.
Peculiar velocity perpendicular to our line of sight changes their location on the sky, but is way too small of a shift to be measured. The radial component of it measurable, as a Doppler shift. That shift is in addition to the redshift caused by cosmic expansion, which is why galaxy clusters in redshift-derived maps like this one
to appear smeared radially. But otherwise none of these motions change the observed galaxy position over human timescales.
The expansion does have an interesting side-effect though in that it changes the relationship between distance and apparent angular size of an object. If you try calculating the size of a galaxy in the usual way as its distance times the tangent of its angular size, then you'll get the wrong answer (and more severely so at greater distances -- beyond a certain point the angular size even starts increasing!) In cosmology we define a new "angular diameter distance" to correct for this, so that the Euclidean relationship holds.
Gnargenox wrote:From what I can tell I think the distances to catalog objects are generally given in terms of light travel time. At least, for the few distant catalog galaxies that I checked which have redshifts, I get good agreement between the stated distances and what I calculate for light travel time in a flat LCDM cosmological model with Omega_M = 0.3 and H0 = 70 km/s/Mpc. The comoving distance would be slightly greater.
Source of the post
The distance noted on the left side of the screen to other galaxies is the distance (time) light has traveled or is it a comoving radial distance for right now? Meaning, is the expansion of the universe included?
However, the catalog galaxies in SE are nearby enough (redshift z less than about 0.2) that the difference between their distance in terms of light travel time or by comoving distance is very small -- I would even say it is unimportant. In fact the uncertainties in the cosmological parameters (like the value for Hubble constant) can matter more.
What about the distances for procedural galaxies? For them I would say its up to your imagination. So far, Space Engine shows the cosmic expansion effect of reddening the color of distant galaxies. Although the SE universe didn't really expand or simulate the light travelling to you, if you like to think that the light is redder because the space expanded and so those galaxies are actually farther away than you'd think from light travel time, then go for it!
I would call the Space Engine universe a static, flat, Euclidean rendition of the universe. There are still some cosmological expansion effects that are not shown, even aside from having the universe grow larger with time. (Like the weird way angular sizes are distorted over great distances that I mentioned earlier.)