I know people during the WWI reffered to it (WWI) as the Great War, and the term world war wasn’t used those days. When did people realize that the conflict was global and called it “World War”?
While more can always be written, you may be interested in this previous answer of mine which talks about both the origins of the names of WWI and of WWII.
This sub's FAQ also has a shorter answer of mine which addresses the history of the name of the First World War alone.
To summarize again: "Great War" was never the only term used to identify WWI. The term "World War" was coined as soon as the war started, and was interchangeable with "Great War" well before the war had ended in 1918, particularly in the United States. By the end of the war, many if not most U.S. newspapers/news outlets were referring to the conflict as "the World War" or "World's War", though "the Great War" was still in regular use, too. In 1919, the U.S. State Department adopted "World War" as its official name on all government documents, and "Great War" fell out of favor rapidly after that in the United States. By mid-1920, newspapers such as the New York Times were using "World War" exclusively to describe the recently-ended conflict.
The "Great War" term had more lasting power in Canada and, in particular, the UK, but even in both of those countries, "World War" was widely understood as a name for the war by the end of the 1910s, if not quite the term for it as it was in the United States. By the mid-1930s, with an increasing threat of another war, even in those countries, "World War" began to displace "Great War" almost entirely.
From the earliest news reports of Germany's invasion of Poland in September 1939, the new war was described as "the Second World War" or "World War II" in the Anglosphere. No other name ever really caught on. Predictions of such a follow-up war, following the first "World War", had been around for years by then.
u/lord_mayor_of_reddit has already given a very thorough answer. I'll just add a couple of things about the presence of the concept of "world war" in pre-WW1 media and literature, because it was rather popular... A the turn of the century, a combination of nationalism, world events, and progress in technology prompted writers to imagine various scenarios for a world war, that usually included a European war, some input from the United States... and hordes of vengeful Asians and Africans.
In the French-speaking media, the term "Guerre mondiale" emerged in 1899 affter a conference of the former priest Hyacinthe Loyson but only really picked up in 1914 after the war started: here is a chart of its occurrence in French newspapers from 1899 to 1920. In June 1899, Loyson gave a series of conferences about disarmement, which included apocalyptic visions of a coming world war:
The War, but a war which [...] would have the character of a cataclysm, because it would be waged under conditions hitherto unknown and truly gigantic: the number of combatants, the nature of the engines of destruction, the enormity of the daily expenses. Both victors and vanquished would be equally decimated and ruined. [allusions to the Four Horsemen of the Apocalypse] This war, indeed, from the Rhine to the Bosphorus and from the Bosphorus to the Far East, and everywhere, on all continents, on all oceans, this war, constantly enlarged by multiple and complex interests and passions, would mix all peoples and all races, all civilisations and all barbarities. The world would be devastated. In any case, Europe would perish.
French newspapers reported that the audience applauded this description of the "world war".
For Loyson, this world war was caused by European colonialism, which had brought to Asian and African people many evils such as violence, greed, religious fanaticism, atheism, alcoholism, and the "debauchery of the colonists". If Europeans were not careful, "Blacks and Yellowmen", the "most prolific races of the world", would vanquish and tame them all, economically and militarily, and they would create a new civilisation where Europeans who pray to Buddha.
During the first decade of the 20th century, nationalist German writers did help with the popularization of the term. The first one was August Niemann: in his nationalist fantasy novel Der Weltkrieg - Deutsche Traüme (The World War - German Dream, 1904), he imagined that Germany, France, and Russia were allied against Great Britain. He wrote in the foreword:
My dreams, the dreams of a German, show me the war and victory of the three allied great nations, Germany, France, Russia, and a new distribution of the possession of the earth as the final goal of this tremendous world war.
In Der Weltkrieg, the Allied fleets destroy the British Navy all around the globe. German, French and Russian troops under the command of Wilhelm II land in Scotland and Southern England, and the Kaiser arrives victorious in London. The novel was translated in English as The coming conquest of England.
Another notable German novel was Ferdinand Heinrich Grautoff's 1906 - Der Zusammenbruch der alten Welt (1906 - The collapse of the Old World, 1905). In this novel, set in 1906, wily Americans create an incident in the Samoan Islands (!) that quickly escalates and makes the German and British fleets fight each other. The Germans end up fighting a French and British coalition, and win a gigantic battle where 400,000 Germans beat 600,000 Franco-British troops. Like in Loyson's fantasy, the "Black and Yellow races" revolt (at this point, French critic Robert Villiers notes in his review of the book: "one really wonders why") and start slaughtering white people everywhere. This wakes up the Europeans, who unite against the uppity Asians and Africans. Germany is the major winner of the world war, and all other European nations redistribute bits of territories between themselves. Russia becomes the main military power and the United States, who planned it all, becomes the only trading power. The defeated Great Britain no longer has a Navy. For Dülffer and Léger-Croenne (1993), the novel was a call for European unity against the US, Russia, and Japan.
In the French newspaper Libre Parole, its antisemitic editor Eduouard Drumont was on a similar line of thought after witnessing the Russo-Japanese War (he blamed the Dreyfusards for making France unprepared):
We have seen the beginning of the most dreadful war the world has ever seen. We are on the eve of a tremendous clash, no longer between two nations, but between Asia and Europe. The peoples are feverishly arming themselves for world war.
Another German author who wrote "world war" books, though these were military essays rather than novels, was Rudolf Martin, who depicted global aerial warfare in Stehen wir vor einem Weltkrieg? (Are we on the brink of a world war, 1908) and Der Weltkrieg in den Lüften (The World War in the Skies, 1909). Indeed, aerial warfare became a major plot point in this genre of "future war stories" that became popular in Europe in the years leading to WW1 (Clarke, 2017). H.G. Wells' The War in the Air (1908) has Germans fighting Americans, and then other European countries, but, like in other stories mentioned above, the feuding "white races" find themselves under attack by Asian forces, and civilisation collapses. Finally, we can cite La Guerre Infernale (1908), an "adventure novel" serialized in 30 episodes, written by Pierre Giffard and illustrated by visionary artist Albert Robida (who also wrote several proto-comic books about the "War in the XXth century"; Robida regretted his techno-war fantasies after he lost a son in WW1). At the beginning of the novel, a character says:
But of course, Sir, war can only be global! For fifty years and more, my father always says, Europe has not seen nations killing each other. Because the armaments of each power are so formidable that it is a matter of who will not risk offending his neighbour. [...] Surely, surely, the war which was being prepared, which had already begun, even in the savage way we know, by the burning of a neutral city, would be, before twenty-four hours, a world war, the monstrous conflagration of the two hemispheres!
The novel follows the now classic plot: Western nations fight and destroy each other, until an Asian coalition steps in and conquers the world, killing and torturing everyone the Chinese way (gory pictures included), including the heroes... but it was just a dream!
All these "fantasy wars" may have helped popularize the concept of the world war, and WW1 was recognized a such as soon as it started. For the Czech-Austrian Marxist Karl Kautsky, writing in L'Humanité (1 September 1914), the current world war was "born out of imperialism" and was going to include the United States, Asia and Muslim countries. For others, it was "the whole world against Germany". The regional newspaper Le Bourguignon wrote on 10 September 1914:
This is not a European war: it is a world war. On the battlefields of France, there are or will soon be soldiers coming not only from all parts of Europe, but from all five parts of the world.
In Geneva, a new daily was published on 1 September 1914 - in a somewhat opportunistic way... - with the title La Guerre Mondiale.
THE WORLD WAR- a title, alas! that we would have liked never to write
In November 1918, French newspapers wrote about the end of the "world war", and even made titles using the term.
In France, the term "Great war" (Grande Guerre) was applied during WW1 but surged immediately after the war and remained popular in the interwar.
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