Absinth versus Absinthe.
One is a brand name, one is the correct generic name. By brand name I mean a producer uses it to refer to theirs. Will get back to you which way round it is.
...two minutes later:
Q. Why the different spelling of Absinth / Absinthe?
A. Absinthe with the "e" is the French spelling, but since 1914 Absinthe in France has been illegal, so most production of Absinth moved to Eastern European countries such as the Czech Republic (formerly Czechoslovakia) where they do not use the "e", so the spelling is ABSINTH.
Source:
http://www.seborabsinth.co.uk/faqs/absinth.asp
(Sebor is a brand sold widely in the UK).
N.B Re the brand name/generic thing I said earlier(!), to further confuse things; it is a brand name thing for the company Sebor. I.e. Sebor Ltd. have a product the called "Sebor Absinth". Which is an absinthe as opposed to a tequila spirit.