Moonshine is only truly spirits that are made illicitly. Everclear is simply a high proof spirit that is commercially made. Of course, as it is often labelled as moonshine or used in lieu of moonshine in many popular moonshine recipes, many want to try Everclear. With 95% alcohol content, Everclear is very potent.
Properly sealed jars of moonshine do not need to be stored in the refrigerator until they are opened. Some people even store their moonshine in the freezer. There, it can last 2 - 3 years.