Holocaust as a term for the destruction of the European Jews by the Nazis (and others) during WWII began almost immediately, but this can be confusing. The term holocaust (lower case) was used to depict any large-scale destruction. It had been applied to the Armenian genocide before the Shoah occurred. This use of the term for the destruction of the Jews, in conjunction with a number of other terms, continued until roughly the Eichmann trial of 1961. It was at that time that holocaust was given to mean the destruction of the Jews in particular. Within ten years, it was primarily used in a capitalized form and was very strongly associated with the unique assault upon the Jews.

Novick, Peter. The Holocaust in American Life. Boston: Houghton Mifflin Company, 1999.

The word "holocaust" had a definition separate from meaning genocide, for hundreds of years. It's from the Greek. "Holo-" which means 'whole', like holistic. And "-caust", which means 'to sacrifice by fire', like caustic. Together, the word "holocaust" referred to a sacrifice to the gods of all of the animal (as opposed to the more common sacrifice of the parts of the animal that aren't eaten, while the people eat the edible parts.

When it was happening and right after, a name hadn't been settled on. In Hebrew, the word "shoah" was used. It means "catastrophe" in Hebrew. Also used was "Churban" in Yiddish, which means destruction. One of the first books on the Holocaust was Unzere Churban in Bild --Our destruction in pictures. Spelling is different for Polish and German but same root word. Sometimes referred to it by the Nazi term--the Final Solution.