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"Moving apart" and "distance between them is getting bigger" are
synonymous, though neither is a "reason" in the causal sense.
These concepts do not have to be synonomous. I think in the context in
which Jim was trying use these concepts is that he meant "moving apart"
to refer to motions that increase the separation between objects as
denominated in comoving coordinates (i.e. an increasing comoving coordinate
spatial separation with time), and he meant "distance between them is
getting bigger" as meaning that the physical proper spacelike geodesic
distance between the objects increases from one spacelike time slice to the
next spacelike time slice.