I mean, WWI was initially "The Great War," or "The War to End All Wars." In the beginning of WWII, did people think of it as the "sequel" to WWI? If people is too broad, then how about the American and European press?
This is in the FAQ for the subreddit.
The answer I gave the last time it came up:
The first place to start answering your question is with another question: When did people start calling it the First World War?
/u/NorseWinter had a good answer to this question when he came up with Deutsche Kriegslieder, which was published in 1914.
On September 20, 1914, the Indianapolis Star ran a wire service report that includes the first known mention of the term "First World War." It quotes the German philosopher Ernst Haeckel, who claimed, "There is no doubt that the course and character of the feared 'European War' ... will become the first world war in the full sense of the word."
Now that we've established that the world wars can be numbered, this leads us to your question. If there was a first war, that implies a second (or third, etc.) The Oxford English Dictionary's etymology for World War 2 points to the Manchester Guardian of Feb. 18, 1919 as the first mention of the term. In that article, the Guardian was discussing the possibility of future wars arising from the upheaval caused by the Great War. During the interwar years, there's plenty of speculative fiction that talks about the possibility of a Second World War. Heck, James Thurber's "The Last Flower" (published in 1939) mentions a "World War 12" as part of its antiwar satire.
What about the actual Second World War?
The first organization to label the war as we know it was Time Magazine, which used the term in its Sept. 11, 1939 issue.
EDIT: Having commented this I see that /u/The_Alaskan has left his answer, but I think mine goes a little more in depth, or at least explores in an interesting way.
Well, here goes nothing: I'm mainly referencing the New York Times, so this is not going to be as comprehensive an answer as possible. I will be referencing The New York Times Complete World War Two (ISBN-13: 978-1-57912-9446). I don't have page numbers of the actual articles in the paper, however I have pictures of the article, the title, author, and page number in the book instead. The linked image
On September First, the opening of hostilities, the Times refers to a possibility of "general European war" ^1, Ferdinand Kuhn Jr. states "At midnight the British Government was not yet convinced that Germany really intended to attack Poland and provoke a world war" ^2
So, September 1, 1939 appears to be the first reference, in the New York Times at least, of the 2nd world war being referred to as a possible World War. Wikipedia gives a time magazine article from June twelfth, 1939^3 .
On September 10th, 1939, the New York Times ran two articles, James B. Breston's "All of Life in Britan Transformed by War" which states that "One man expressed the opinion of the public pretty well yesterday when he wrote to The Times of London suggesting that everybody agree to call this "Hitler's war."^4 While Allan Nevins, a professor of Hostory at Columbia University, wrote an op-ed entitled "Can Civilization Survive a World War?"^5 which is exactly what it says on the tin. This article, while not referring to the 2nd World War as such, does describe a coming world war as destructive to large swaths of Europe.
^1 Jerzy Szapiro, "Germany Attacks Poland, Hostilities Begun" p32 (last sentence of article)
^2 Ferdinand Kuhn Jr. "British Moblizing" p32 (fourth paragraph of the first heading)
^3 behind a paywall, but at this link
^4 James B. Breston "All of Life in Britan Transformed by War" p47-8
^5 Allan Nevins "Can Civilization Survive a World War" p49
Pictures!
1, 2, here
5: Image
A question to those better informed than I am, similar to OP's question: When did the terms "World War I" and "World War II" first come into contemporary use? What about the "Cold War"?
