Mystery Solved.

The Latin word for such vernaculars was theodisce. On the British Islands it was used as a name for Old English. In Old High German there was the term diutisc, in Middle High German tiutsch or diutsch. Therefore, “Deutsch” can be translated to “the language, spoken by the (common) population”, in opposition to Latin. Later on, the term was used to differentiate between romanic and germanic languages. In the 10th and 11th century Diutisc and tiutsch were used as a name for the germanic languages spoken on the continent. Even dutch dialects were called “Deutsch”. The Englisch word Dutch is a relict of those days. Today German and Dutch are different but similar languages.
But why are the words for German so different? In the list above you can discern four different groups. Some are related to the word deutsch. For instance Italian tedesco, Dutch duits or Swedisch tysk . Those languages use a form of the self-designation german speakers use.The English word German comes form Latin. Julius Caesar used the word Germani to speak about tribes in the north-east of Gaul. The precise origin of the word is unknown. It might have been the name of a particular tribe.The French and Spanish words are derived from another group of tribes, called Allemanni. They lived in the region we call Alsace today.The forth group of words ( like Czeck německy and Polish niemiecki) might have been derived from the name of another germanic tribe. The Nemeter lived in the region of Lake Constance. But this explanation is not uncontested.

This is where 'Tedesco' comes from...