I still don't know when it is correct to use "The Organisation" and when to use "The Society"
They are interchangable, and any JW will know what you mean when you use them, although neither term is currently en vogue amongst active JW's. The currently used term is "The Branch", as in, the US branch, the UK branch, etc. There was a directive to use that term rather than the older terms, probably because "The Branch" seems less like a mystery cult then "The Society" or "The Organization". These directives are announced from time to time, I remember about fifteen years ago there was an announcement at an assembly that simply said: "Please say 'New World', not 'New Order'". The explanations for these changes in terminology are never given to the rank & file to my knowledge.