Scotch whisky has always been traditionally spelt without an ‘e’ whereas Irish and American producers do add an ‘e’. There are several theories about the origins of the spelling which range from the original translations from Scots and Irish Gaelic to the simpler explanation that the Irish kept the ‘e’ to help differentiate their product from Scotch and when Irish immigrants crossed the Atlantic they took their spelling with them.
It must be noted however that there are a few Irish whiskey brands who have changed from using an ‘e’ to dropping it entirely. The same goes for American whiskies – again a country that has historically used an ‘e’ in its spelling but also has several producers that use the Scottish spelling.
Japan is another country that has always eschewed the ‘e’ but I can imagine that it relates to the respect and the regard Scotch whisky is held in by the Japanese, Japan famously sending over its leading distillers to learn their trade from us before taking the knowledge back home to their own stillhouses.
Previously the best way to remember which was which was that countries with an ‘e’ in their name use an ‘e’ in the spelling of their whisky. This however is now not always the case as whiskies from counties such as England, France, Czech Republic, Germany and Sweden are themselves electing not to use the ‘e’