I may be misunderstanding the nomenclature; I have just always wondered how exactly (technically) can a single mesh contain multiple materials at once.
Yes and no... While you can assign a material to certain vertices and they can then be selected that way, vertex groups, as used by Blender, are actually separate from the materials. So you can have vertices that have the same material, but are in different vertex groups. In fact, you could even have vertices that have different materials but are in the same vertex group. All a vertex group really is is a collection of vertices that are put together in a group and given a name. There are lots of ways that could then be used. As for the materials, the vertices that are assigned to a material are just so that Blender knows which materials to use with which vertices.
Yes it is similar to vertex groups, but it would be more like a face group. Since you actually assign the face to the material slot. Technically speaking each polygon is made up of a bunch of parts. Like a face and the face's number(Instance), which material slot the face is assigned to. It also has the number of edges that make up that face and their numbers. Then there is the vertices and there numbers along with each one's position in the meshes local space. Each vertex is also assigned a color. This is what vertex painting is used for. There is also information on face corners, but I believe that is stored at the object level not the individual polygon. Martian would know better than me on this.
Yes, like Dwayne says, Material Slots are assigned to Faces, as you can see here:
So, for instance here, the Face with Index 5 is using the Material from Slot 2 (the third Slot, because the first Slot is 0), blue.
Face Corners are mainly used in UV's.
There are also Vertex Colors, which can be per Vertex, or per Face Corner, but that is a topic for another day, I think.
I have always thought about it like each face being its own individual person, so you can just assign information to them separately. In object mode (the container of all that information) things may look like a solid single thing, but all those faces that make up the whole object can be used for all sorts of trickery. One of them being assign a material per each face. The other shave given technical answer, but I always like to think of stuff in metaphors, so the faces I think of as dudes with different t-shirts and each t-shirt of different colors and you can take on and off the t-shirt for other colored t-shirts. Kind crazy.
Yeah the crazy thing is that polygon and face are used interchangeably, but a face is technically only one part of a polygon. Omar, I also like metaphors. I think of it as each face is a piece of paper. you can swap the paper for different colored paper. I like your T-shirt one. I'm going to use that the next time I'm teaching blender to someone.
If you'd like to differentiate between a Polygon and a Face, I'd say a Polygon is 1-dimensional (like a circle) and a Face is 2-dimensional.
Or, a Face is what you can Select in Face Select Mode and a Polygon is the Edges of that Face.
But I almost always use the terms as being interchangeable. Nobody will call the CG police on you.
And now we can also say that a Face is a dude (or a piece of paper) 😉