The problem is that distant observers cannot directly measure distances or times; only a local observer can do that. Distant observers have to set up some sort of convention for assigning cooridinates to distant events, but those coordinates don't usually directly measure distance or time. But the coordinates come with a metric which tells you how to convert coordinate differences into distances and times. Note that even these distances and times are in general "coordinate dependent" because there's more than one way to decompose spacetime into space+time. GR is rather more flexible than SR in this regard. In SR it is generally agreed that there is only one way that we usually decompose spacetime into space+time relative to a given inertial observer, but in GR there are no truly inertial coordinate systems and there's much more choice about decomposition.
If you are simply looking at the coordinate values and ignoring the metric, interior coordinates are not the same as the "coordinates at infinity" (assuming you splice the different sections together to ensure continuity at the splicing points). In this case the interior metric will be of the form[tex]ds^2 = A^2 \, \, dt^2 - B^2 (dr^2 + r^2(d\theta^2 + \sin^2 \theta \, \, d\phi^2))[/tex] for some constants A
chosen to get a "smooth splice", or, in Cartesian form[tex]ds^2 = A^2 \, \, dt^2 - B^2 (dx^2 + dy^2 + dz^2)[/tex]If you apply the metric, the "interior" distances will be the same as those "at infinity".