Have a look, what I found:
"Embassy" is actually a variant of the word "ambassy" - just a different vowel, but it has the same root as "ambassy" .
Both ambassador and embassy come from the Latin word ambactus, "servant". Going further back in time, the etymology becomes murky. According to the Oxford English Dictionary (2nd edition), the Latin word may have been derived from Celtic, but that is uncertain. Alternatively, it may come from the Proto-Germanic precursor of modern Dutch/German ambacht. But most etymologists hold the view that the Germanic word must have been derived from either the Celtic or the Latin word.
source: English Language & Usage Stack Exchange
Wer eine Fremdsprache lernt, zieht den Hut vor einer anderen Nation.