The generally accepted principle for the start of WW2 is September 1, 1939, when Germany invaded Poland.
I'm sure the Poles would disagree but I've always thought of it as the 3rd September, 1939, when Britain & France officially declared war on Germany.
As for the description World War, this involved not only most of continental Europe but also the whole British Empire, French colonies & colonies of the Axis powers, covering a large part of the world. This map gives some idea of the scale.
Map with the Participants in World War II:

Dark Green: Allies before the attack on Pearl Harbor
Light Green: Allied countries that entered the war after the Japanese attack on Pearl Harbor.
Orange: Axis Powers
Grey: Neutral countries