What is the difference between a range image and a depth map? https://en.wikipedia.org/wiki/Depth_map

https://en.wikipedia.org/wiki/Range_imaging

To me, it sounds like they are the same thing, except depth map implies only having the z coordinate info.

But then again, if you have a range image vs depth image, is this something one can tell the difference by examining the data or is the term mostly contextual?
Your understanding is correct, it's z-values vs distances.

A depth map contains the distances of points in the scene to a plane.

A range image contains the distances of points in the scene to another point. This point is very often the camera's position.

For a depth map the plane that the distances are computed with respect to can be any plane, but it is often parallel to the image plane. Examples of common planes:


The image plane
The focal plane
A plane closer to the object, such that the points closest to the camera have distance zero.


If you of the same scene have:


A range image with the distances to the camera
A depth map with  the distance to the image plane


these two images will look very similar, and it's not possible to conclude whether it's a range image or depth map, unless you have something you know is a plane in the image.