There is a big difference between Hail and snow. Specifically in terms of size, hail and snow are not the same, although the two are frozen crystalline state of water. When you are talking about snow, you are referring to one or more tiny ice crystals dropped during snowfall. But hail is typically different in that, it is a whole lot bigger than a pure ice crystal or snow. What set the difference is their pattern of formation. Snow is formed when water vapor is cooled and directly turned to solid through deposition process i.e there is no liquid state.
Snow can occur during rainfall and it can also form during thunderstorm. Depending on the temperature, humidity, and other conditions within the cloud, there are about 80 possible formations of snow, meaning there are different types of snow crystal formation. But when it comes to hail formation, it only happens during thunderstorm. The balls of ice through precipitation that hail represent can also be formed in cumulonimbus clouds.