How do you tell the difference if all you can do is look at 1a supernovae redshift?

If it was just standard motion, we’d expect to see a more-or-less random distribution of rates as we looked around: some things should be getting closer, some things should be moving away slowly, and some things should be just hanging out. That’s not what we see. Instead, no matter where we look, it appears that everything is receding from us at a rate that is proportional to distance–the further away something is, the faster it is receding. Since we assume that we aren’t in a privileged position in the universe (that is, we assume we’re not at the center of the universe), the best available explanation is that the actual distances are expanding. The further away something is, the more space there is between us and it, and so the faster it appears to recede. Since we’re not in a special position, that means every other observer anywhere in the universe should see the same thing.