It's called a world war in english because everyone and everywhere was at war during that time. Pretty much every group has a name for it in their own language.
What's the difference? They were involved in what is colloquially known as WWII. They just refer to their specific part differently amongst themselves, but they certainly did have WWII.
The Soviet Union did not have WWII. They had the Great Patriotic War of 1941-45.
There is a difference there.