Simple Diffusion (or just "diffusion") is a process by which molecules of gas or liquid move from an area of high concentration to low concentration until equilibrium is achieved. If you open a bottle of oxygen in a room, the oxygen molecules will be concentrated near where they were released, but will eventually spread out around the room.
Osmosis is similar to simple diffusion, but it describes water molecules moving across a membrane, which allows the water molecules to pass in and out freely, but forbids the motion of other molecules.
Facilitated diffusion is a process that allows molecules that couldn't normally cross a membrane to cross it with the assistance of transport proteins, which act like gates, having receptor sites to "invite in" certain molecules and keep out others.
All three processes are examples of Passive Transport, meaning that no energy is expended to move the molecules; none of these three are special cases of the other, but one could consider that Osmosis is Facilitated Diffusion without the special transport proteins.
Osomosis is Diffusion inside the permeable membrane.