If those redshifts differ, then we might say the speed of the galaxy has changed and thus that the galaxy is accelerating. There are various other, indirect ways to try to look for this sort of acceleration, though, and some of them seem to have yielded positive results. The measurements essentially involve plotting the redshift of galaxies against their distances, as inferred by the brightnesses of supernovae in the galaxies. The shape of this curve depends slightly on the way the expansion rate varies with time. That is, if something is in free fall, with no significant nongravitational forces on it, we say it's not accelerating.
Nobody knows for sure.
If the experiments had shown that the galaxies were slowing down, then it would have been natural to explain that as being due to gravity. The fact that the evidence suggests positive acceleration is somewhat puzzling. That's probably the simplest explanation, but no one knows for sure whether it's right.