The difference between ginger ale and ginger beer is the former typically uses a ginger extract, whereas the latter uses fresh ginger, be it juice or otherwise.
Typically, ginger ale has a more delicate and subtle ginger profile, with dark or caramalised sugar base. This makes it more suited to compliment top-shelf whiskey, whereas ginger beer may be better suited in a cocktail such as a Moscow Mule or Dark n Stormy - where ginger is the star.
To summarise, Ginger Beer is like Ryan Gosling or Harrison Ford, whereas Ginger Ale is more like Danny Devito - there to make the other players look good. Check out our versions of Ryan Gosling Lo-Cal Double Ginger Beer and Danny Devito Dry Ginger Ale.