Terms of Reference-1939-1945

[Jon Skagfeld]

At a recent military conference, I was told that Commonwealth countries referred the the 39-45 unpleasantness as "The Second World War", whereas the US referred to it as "World War 2".

I've never heard of this differentiation; I always thought that the two terms were mutually interchangeable.

Is this an important discrimination to observe, depending upon one's context of reference?