Sup[pose I have a model of a unit cube (12 faces) aligned to the three axes, and another model of a cube divided into thousands of faces and hard-coded in a random orientation. They are both cubes, even if the point cloud and face index are completely different. What is this called? Resemblance? I know there is a term for this, yet I cannot recall it. I'm currently reading about the Hausdorff distance and the Fréchet distance, yet these do not quite pin down the concept in 3D. Thanks in advance.
What is this called?
People give names to a concept when that concept is relevant to their lives. This is why programmers have a lot of technical terms for things that happen in programming, but those technical terms aren't used by people outside of programming.
The concept you describe is not something that really matters to people. Sure, it's a thing that happens, but it doesn't happen often enough, meaningfully enough, to enough people to warrant giving it a name.
You could say that the two meshes are similar to one another, but that's just using regular English definitions.