Originally Posted by Jeff Neese

Both varieties use calipers to squeeze brake pads against a rotating disc, causing friction which slows down the rotation of that disk, to which the tire is attached.

Are you really having trouble understanding a bicycle wheel as a rotating disk? With rim brakes, the braking surfaces of that rotor are simply at the outermost edge of that large rotating disk. Don't let the hollow part in the middle fool you - those spokes are part of the disk. It might be easier to visualize a solid wheel instead of a spoked wheel - then it's easier to see that they are the exact same type of brake, differing only in execution and complexity, and of course the diameter of the disk.