"World War II" - "the Second World War"

Are they mere synonyms?

Or WWII is for "American English" and "Second World War" is for "British English"? (a book has been translated (by a translator who is not a native speaker of English) from Latvian into English, here, in Latvia, keeping to British spelling style.. but I find the two above forms interchanging in the manuscript.. I guess, one of them should be used.. but does it belong to "spelling" and how strictly??)

I don't think it's an American/British thing. Maybe it's just a choice - like using '1000' or 'one thousand'.

There's also 'World War Two', which the BBC uses. The Arlington National Cemetery website uses 'World War II' and 'WWII', but also 'World War One'.

We British may say either 'the Second World War' or 'World War Two' but ' the Second World War' is more commonly and colloquially used .We would normally write 'World War II' not WWII or WW2 unless being informal (or seeking brevity in a post ). Of the brief forms WWII is used rather than WW2 (because of our classical education,the spirit of which pervades every pore of our bodies, of course )

Of course, people here often speak simply of 'the war' because they could only mean the one.

Thank you both, very much.