It can be confusing to keep track of the different processes that items may undergo, especially when you are not too knowledgeable about the various scientific methods. Two of the ways that people may interchange is osmosis and facilitated diffusion. Osmosis usually involves the movement of water molecules through semi-permeable membranes. Osmosis would need water molecules so that the process can take place successfully while facilitated diffusion will allow the process to take place without the need to use water.
Osmosis is also an example of facilitated diffusion. It is just one of the methods that fall under this. Facilitated diffusion can be very vague. This can be the process of making sure that different molecules or ions can be transported properly.