system
Given the following post, respond as if you're commenting on Reddit:
human
Is space the same as distance?

And wouldn't distortions of space likewise distort everything within it to the same degree?
gpt
They are a little different.

* Space is a set of points

* Distance is a relationship between points

In a 100 cm box, you can measure the distance 1 cm in many different places. Are you measuring near the front of the box? Near the back? Or near the center? Distance alone doesn't tell you this.

A distortion (It doesn't have to be as exotic as gravity, just imagine the separation between two dots as you blow up a balloon.) tells you when the relationship between two points in space changes. Essentially, distortion tells you how distance changes.

In relativity, you can't just use euclidean 3D space anymore, but 4D spacetime and thus distance now include the passage of time on clocks as a form of distance.