What’s the different between ‘while’ and ‘whilst’?

‘Why is whilst only ever used in letters?’ asked my husband, casting aside an argumentative letter from his sister written in curly script and blue ballpoint. Why indeed?

It cannot be wrong to use whilst, any more than amongst or amidst. But it goes with a certain register of genteel speech that can merge into officialese or hypercorrectness.

Whilst, amongst and amidst started off by displaying what is called the adverbial genitive.