Osmosis is what happens if you put two solutions in contact with each other, separated by a thin membrane. If both solutions are made of water plus something dissolved in the water, the more pure water will get soaked up by the other water.
It is sort of like what happens when a dry sponge soaks up water as you wipe up a spill. You can do experiments that show this influx of purer water by showing how the water level rises as water is sucked up through the membrane. Just like a sponge can be wrung out, you can reverse this process and, with sufficient pressure, you can force pure water out of salt water.
Reverse osmosis involves high pressure that forces water through a membrane, thus removing impurities. That membrane is a reverse osmosis filter. It is critical to the process of reverse osmosis. The membrane must be strong enough to resist the pressure while it filters the water forced through it. The filter is so critical that desalination technology took a big leap forward in the sixties when two UCLA scientists created a better filter.
These scientists began using cellular acetate to make filters. Yes, this is basically the same stuff used to make film, but repurposed to purify water. Upgrading to this type of filter allowed more water to be processed more quickly, finally making it feasible to run a reverse osmosis desalination plant at scale.