World War 2 "started" on the 3rd of September, when Britain and France declared war on Germany. (They had a treaty with Poland). The war ended in early May 1945 in Europe, Hitler having committed suicide in April of that year. The war in Japan ended after their surrender to the Americans in response to the A-bombs dropped on Hiroshima and Nagasaki - respectively the 6th and 9th of August 1945.
By a long-standing convention, the dates are usually given as 1939-1945, except in Russia, where they are usually given as 1941-1945. If one gives another starting date, one conveys the message that one is making some point or other, for example, that one is claiming that the sufferings of the Chinese have not been given the attention they deserve. As for the notion that WW1 and WW2 were one war with a 20-year truce, this is not meant literally.