There are many different ways to define a distance based on what we can observe from Earth, and each of these definitions leads to a different set of cosmological relationships depending on the type of model you adopt for the geometry of the universe. Dr. Edward Wright has a cosmology website where he discusses these many different definitions and how they translate into algebraic formulae that you can use.
A metric distance is actually not observable, and is what most people think of when they ask 'how far away are galaxies RIGHT NOW'. According to Big Bang theory, which is based on general relativity, every galaxy has a fixed coordinate address which doesn't change as the universe expands. This is like the latitude and longitude coordinates of cities on the Earth. If you inflated the Earth, the latitude and longitude coordinates would not change. The metric distance between them, however, will increase depending on the current scale factor ( radius ) of the earth. If you know how fast the radius of the Earth is increasing, it is a trivial exercise to convert the angular separation between the cities into a linear number of miles. You can then use a tape measure to pace off this distance a foot at a time to verify your calculation PROVIDED the radius of the earth does not change very rapidly to affect the measurement over the time needed to pace the distance.
In cosmology, we can only determine the metric distance to nearby galaxies within a few 100s of millions of light years from the Earth, because for greater times, the expansion of the universe adds a growing 'correction factor' to correct for the fact that what we see NOW is where the galaxy was at an increasing time in the past when the scale factor of the universe was increasingly different from what it is now which by definition is 1.000000
So what do cosmologists actually measure? Well, our messenger is light. So what we are actually measuring is the length of the path taken by light in getting from a distant galaxy to where we are in the here and now. This path is not straight and linear, but of each 'differential' distance element, there is a slightly different cosmological scale factor that applies in the history of the photon. You have to use calculus to integrate all of these differential distance elements over the travel time of the photon/light ray. The net result is that the light travel distance is shorter than the light travel distance. You can convert from a light travel to a metric distance, only if you exactly know what kind of universe you live in and its global geometry.
Do cosmologists need to know the metric distance? No, because from the various observable distances you can always express them in terms of the completely unobservable metric distance. You should realize that for us, it is only the light travel distance that is physically important. It determines how long it took for a distant galaxy to influence us gravitationally. A galaxy influences us based on where it was a light travel distance ago, not where it is right now at its metric distance.