This is quite simply a language difference. Although 'absinthe' is the generic spelling as coined by the Swiss and French, who were the original absinthe producing nations, you will find that around the world there are many different spellings for the word absinthe. In the Czech Republic 'e' is dropped, and thus, absinth. The Spanish say absenta and the Italians say assenzio, but they all mean absinthe. Absenth does not mean anything, it is just an incorrect spelling.