The Elixir is a different formulation. It is a gourmand version of the Eau des Merveilles. Here are the notes for the Elixir: chocolate-covered candied orange peel, caramel, vanilla biscuit (vanilla sugar, tonka bean), creamy milk, sandalwood, incense, resins, ambergris, Peru balsam and balsam of Siam, oak, patchouli and cedar.
It's supposed to be, but I found the elixir to smell like fertilizer. EDT smells way better.
Yes, to the best of my knowledge Elixir is parfum to EdM. I've tried it but always go back to EdM. Strangely, Elixir doesnt stay all day on me like EdM does.
Hope this helps!