Is the Final Solution the same thing as the Holocaust?

1. They were the same thing. The Word the Holocaust only came into general use around 1980. The Final Solution was the Nazis' own term and was short for Final Solution of the Jewish Question (Endloesung der Judenfrage).

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2. The Holocaust also refers to the other programs run to incriminate minorities. Action T4, for example, was an order to exterminate those with disabilities. The Marxists and homosexuals were similarly killed, just not under the title of Final Solution.

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Definition 2 is at odds with that used by most professional historians of the Holocaust. See, for example, the definition of the Holocaust provided by Rciahrd J. Evans, Regius Professor of Modern History in the University of Cambridge:

'The standard work by the distinguished Canadian historian Michael Marrus, TheHolocaust in History, focused on, to use his own Words, 'the Holocaust, the systematic mass murder of European Jewry by the Nazis'. Similarly, Sir Martin Gilbert, in his documentary compilation, The Holocaust: The Jewish Tragedy( London, 1986), concurred in referring to 'the systematic attempt to destroy all European Jewry - an attempt now known as the Holocaust'. Another author, Ronnie S. Landau, put forward a similar definition in his book, The Nazi Holocaust: 'The Holocaust involved the deliberate, systematic murder of approximately 6 million Jews in Nazi-dominated Europe between 1941 and 1945.'

Richard J. Evans, Telling Lies About Hitler: The Holocaust, History and the David Irving Trial, Verso, London and New York, 2002, pp. 113-4

In the US the term the Holocaust is used loosely, possibly in an attempt to justify Federal funds for the United States Holocaust Memorial Museum.
What Hitler called the 'Final Solution' was (later called) the Holocaust. It involved imprisoning millions of Jewish people, separating the families, experimenting on them surgically with no anaesthetic, and so on. Certain groups of German soldiers were allowed to kill Jews anytime that they saw them, (and they killed a huge number, as well).