English translation: thesis (US) versus dissertation (UK)
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"A dissertation embodying results of original research and especially substantiating a specific view; especially : one written by a candidate for an academic degree."
and a "dissertation" as:
"An extended usually written treatment of a subject; specifically : one submitted for a doctorate."
From this I would gather that the "dissertation" is for the doctorate and the "thesis" is for the Master's = Diplomarbeit/Magisterarbeit in the US.
The above supports most of the previous answers and agrees with usage by my British and American friends who have written such things. As an American, I have referred to a Master's Thesis and Doctor's Dissertation all my life.
This unfortunately means you may have to tailor your choice of terms to suit your audience. As long as you write the word "Master's" in front, everyone should understand either term.