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.