We get asked this question all the time, the short answer is, Rum is made from Sugar Cane, Whiskey is made from some kind of grain and moonshine is made from corn.
Now that being said, Rum is made from sugar cane but that could be molasses, cane sugar, brown sugar. It can not be made from beet sugar. That rule is pretty strickt. Rums made in different parts of the world are going to taste different also. In the Caribbean rum is thicker that is because of the weather hot and sticky. Rum is one of the oldest alcohols in the world. Sailors used to get a ration of rum with their pay.
Whiskey is made from grain. It could be any kind of grain, Corn, Rye, Wheat, barley or a mixture of all of them or some of them. To be called bourbon it has to be 51% corn, to be called a Rye whiskey it has to be 51%rye. There is actually a whole set of rules before whiskey can be called bourbon.
Moonshine is usually made from corn, it is unaged. Generally it is distilled, bottled and flavored kind of all in the same motion. The corn makes sugar which will make alcohol or higher the alcohol content. People have it in their head it is some kind of scary thing that will make you crazy or something. It is not, the name comes from prohibition times when people would make it out in the woods by the light of the moon to keep the revenuers off their backs. Look into your family history I would bet there is at least one moonshiner in there.