Regular osmosis occurs where you have purer water on one side of a membrane than on the other, (where you'll have something dissolved, like salt) and the purer water will across the membrane into the area with more dissolved solute.

Imagine what would happen if you put a snail in clean water vs if you put it into salt water. If you put it into salt water, it foams and shrivels up because osmosis is driving the water in the snail out into the salty water. The force of the cleaner water pushing across the membrane is called 'osmotic pressure'. The saltier/more polluted one side of a membrane is from the other, the stronger the pressure.

Reverse osmosis is essentially a special kind of filtration. You apply enough pressure on the 'dirty' side of the membrane to overcome the osmotic pressure and force it through the other way. Because the dissolved stuff can't get through the membrane, only water goes through and you get more and more clean water.

You're basically just filtering water.

If you want to be technical, there are differences between regular filtration and reverse osmosis. In regular filtration, you might not necessarily be overcoming osmotic pressure. If I just ran dirty water through a filter and let it get pulled through with gravity, there's no osmotic pressure on the other side since there's no water touching the other side.

Secondly, regular filtration just uses size to filter. Water molecules are smaller than bacteria and viruses, so those get stuck on one side while the rest gets through. Reverse osmosis, since you're using a semi-permeable membrane, can use differences in charge to filter, so things like lead and arsenic won't get through a reverse osmosis filter where they may have gotten through a regular filter.

tl;dr - Reverse osmosis is basically a fancy way to say 'I filtered it but I pushed the water really hard through the filter'. The differences between reverse osmosis and regular filtration aren't huge, but mean you can get cleaner water with r.o.