That is not as dumb a question as it sounds. Let me illustrate.

I address preamble to that war in another place. Here I discuss only September 1939 and following and only major events. In that month Germany declared war on, or at least attacked, Poland. Let us count that as one war.

Then Britain declared war on Germany and France declared war on Germany. There are two more separate and distinct wars. Those can be questioned as there was an announced Tripartite Alliance between Britain, Poland and France against all aggressors to any of them. On one hand we can say there was only one war, Germany against the Tripartite Alliance. On the other hand, since Britain and France failed to honor it we can say there were three separate wars.

Then a couple weeks later Russia attacks Poland and there is a fourth war. As Britain and France dishonored their alliance with Poland by refusing to declare war on Russia as required we have the basis for saying there were three war and the Russo-Polish War is the fourth.

Clearly these are no more than European wars occuring at the same time. We do not even have a single European war as there is no thread holding together other than Britain and France.

Then Poland surrenders to Germany and Russia separately. Thus two wars end. After that there are only two wars active, between England and Germany and between France and Germany. So we go from four wars to two wars with the surrender of Poland.

We note up to this time there has been a war going on between Japan and China for some years. That can not be called an Asian War or a Pacific War. So at this point in September 39 and all over the world, we have five separate and distinct wars that at best we can revert to four by considering the British-French-Polish alliance as one war. But after the surrender of Poland we are back to only two from a peak of five depending upon how we count the wars.

This of course ignores several minor wars such as Russia against Finland, Lituania, Latvia, Estonia and a few other places. So the count is factually a bit higher. But lacking alliances against Russia they are all separate wars. And note of course that Germany attacked one nation, Russia many nations.

Germany invades France and in the process kicks out the British Expeditionary Force putting a legend around the chinese fire drill of Dunkirk. But if we counted France-Germany as a separate war, we have on less war now. And of course Poland fell so those two wars went away. (And the little countries that Russia stepped on.) So we are actually down to one war in Europe, Britain against Germany.

The next milestone being the start of the war between Germany and Russia. Now we are back up to two wars. Around this event, all hell has broken loose. Italy is declaring and attacking right and left. Germany gets involved in some of Italy's follies.

At this point we can count more people and nations fighting than not fighting so we can legitimately say there is a European War not a world war. Even if at this point the US had become involved in the European War we would not have a world war. At best we would have had an anachronistic NATO war. We have no link to the nasty little war between China and its breakaway colony, Japan. At this point all we have at a functional level is an alliance between Britain and Russia against Germany and Italy (and Hungary, Czech Republic, Yugoslavia and Romania as Axis powers.)

The above events are months apart and thus there were legitimate events. Legitimate being that there were intervening diplomatic events that were separate from declaring war right and left. But as a result of Pearl Harbor we get only declaring war right and left and thus our world war.

At about the same time as Japan attacked Pearl Harbor it attacked the British colonies in South East Asia. Thus that spread from just another fued between neighbors to a direct conflict between an asian power and a european power. But still not a world war. That came when Germany honored its anticommunist pact with Japan and declared war on the US on 10 December 1941. And of course that declaration was reciprocated.

That event gives us worldwide linkage. That is the first time we have a world war.

[Sidenote] As the First World War did not meet this clear criteria for being a world war, it was not. It would be correct to agree with russian historians to refer to The Great (European) War, our World War One, and the Great Patriotic War, our World War Two. Of course we could not call our Second one by the russian name.