Right now, we use "local coordinate" to describe a coordinate in an IndexRegion's domain, and "absolute coordinate" to refer to a coordinate in its range. So:
IndexRegion[2..3] has [0] and [1] as local coordinates, and [2] and [3]. are its absolute coordinates (idx_r[0] == [2], idx_r[1] == [3]).
This language is a little confusing, especially for an outsider. I think that "input coordinate" and "output coordinate" might be better names for these? Or perhaps domain coord and range coords? Still unsure about this, but a better name would be good.