Les wrote:
In SR there is the concept of the light cone for which ds^2=0.

Yes.

Does this really mean that in spacetime there is zero distance between any
points on this cone?

Yes.

That is, in some way all points on the cone occupy the same position in
spacetime.

No.

You are mixing levels: "same position" (in the sense of "same point") is
a topological criterion, but "distance" is a geometrical concept. This
is, at base, semi-Riemannin geometry, which means that the metric is not
positive definite. In semi-Riemannian geometry, a given pair of points
can have negative distance squared, zero distance squared, or positive
distance squared; in SR and GR we call these 3 cases timelike,
lightlike, and spacelike intervals (we often use the word "interval"
instead of "distance" to avoid the confusion you just displayed; but
they mean the same thing).


Tom Roberts