I am desperately looking for a scene-wide collections of materials, but I can't find it.
You want scene-wide materials?:
>>> bpy.data.materials[:]
[bpy.data.materials['Material'], bpy.data.materials['Material.001']]
this shows the materials for one object:
>>> bpy.data.objects['Circle'].material_slots[:]
[bpy.data.objects['Circle'].material_slots[0], bpy.data.objects['Circle'].material_slots[1]]
or
>>> [m.name for m in bpy.data.objects['Circle'].material_slots[:]]
['Material.001', 'Material.002']
For completeness then
bpy.data.materials indices
For sake of argument I have a scene with 4 materials
>>> bpy.data.materials[:]
[bpy.data.materials['MAT A'], bpy.data.materials['MAT B'], bpy.data.materials['MAT C'], bpy.data.materials['MAT D']]
We don often need to get the index (in the materials collection) of a material, there's no need to because we can use the name (a string) directly to get the reference.
>>> my_material = bpy.data.materials['MAT D']
>>> my_material.name
'MAT D'
If you really wanted to find the index of 'MAT A' in .data.materials, you could do a .find() because material names are allways unique .
>>> bpy.data.materials.find('MAT A')
0
data.materials is an indexed collection.
>>> bpy.data.materials[0]
bpy.data.materials['MAT A']
material slot indices
The material slot indices refer to the order in which your materials appear in the object's 'material stack'.
>>> obj = bpy.data.objects['Icosphere']
>>> obj.material_slots[:]
[bpy.data.objects['Icosphere'].material_slots[0], bpy.data.objects['Icosphere'].material_slots[1]]
If you want a direct reference to the material in a slot, boom. its easy too.
>>> obj.material_slots[:][0].material
bpy.data.materials['MAT A']
No need to get the name first.
>>> obj.material_slots[:][0].name
'MAT A'
If the material_slot_index is 1, and I have two materials referenced by the object (MAT D and MAT C), then 1 refers to MAT C and globally MAT C is index 2. I may be a point of some confusion that the term index is used to talk about the location of an item in two different types of collections.
Different Materials assigned to different faces
>>> bpy.data.meshes['Icosphere.001'].polygons[42].material_index
0
this zero refers to the material slot index.
>>> ico_mesh = bpy.data.meshes['Icosphere.001']
>>> idx = ico_mesh.polygons[12].material_index
>>> ico_mesh.materials[idx] # get the reference
bpy.data.materials['MAT D']