First off, they are both made of water. Ice is frozen water (lower energy state of the mo9lecules causes the intermolecular forces to become stronger, changing the liquid to a solid). Fog occurs when water from the air cools down, collects into droplets, but don't become large or heavy enough to actually "fall" out of the air. Fog is a liquid version of water that comes from water vapor (gas version of water). When the temperature drops, the gas molecules move closer together and become fog. If the temperature drops enough, it can go from the liquid to the solid version of water. Fog is generally found closer to the Earth's surface. Ice can happen anywhere from the Earth's surface up into the atmosphere. Attached is a great experiment on how to make fog at home (on a small scale).