How do facilitated diffusion and active transport differ? Is osmosis an example of facilitated diffusion or active transport?

Note that Facilitated diffusion, Active transport and Osmosis are three different ways of transporting substances across the cell surface membrane.

Facilitated diffusion is the movement of a substance from high to low concentration, similar to simple diffusion, but due to the complexity of the cell surface membrane, polar molecules and ions cannot just pass like that, so they pass through specific carrier and channel proteins in the cell surface membrane and so we call it facilitated diffusion.

For Active transport, it's the movement from low to high concentraion using energy from ATP

For Osmosis, it's totally different. You only name osmosis when its all about water. Its the net movement of water from high water potential to low water potential through partially permeable membrane.

If you're doing AS, you'll be familiar with Endosmosis and Exosmosis.