What are multi-stage pastry molds called?
There’s nothing special about the mods, they are just various kinds of spherical molds.
I am quite sure that the different materials has to do with different use cases (some have to be oven proof, others not), but probably more with what manufacturer offered which diameter. If the chef is aiming for a specific layer thickness, they’ll have to find the corresponding sizes, and just go with whatever material they are made of.
Looking at my collection of kitchen tools, I have over time amassed round cookie cutters in different diameters, materials and heights, and will just grab what size I need for the given project. I would assume the same is true for the spherical molds here.
More details, as you insist that I must be mistaken, here a list of similar products (no endorsement or claim that these are the same):
First step (baked center) could be something like this
Various diameter molds (with holes, as you emphasized) for example here in silicone, I am sure there will be other models in other materials.