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 carmelised sugar base. This makes it more suited to compliment top-shelf whisky, 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.
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