Q From Gary Wade: As an American who has spent some bit of time with British English, I have always wondered about the difference between while and whilst. Is there a relationship to formal and informal tenses left over from Old English? I also think of amid and amidst.
A You’re close to the target with your second example. Another pair of a similar kind is among and amongst (a third pair, again and against, has a similar origin but the sense of the words has since diverged).
In both cases, the form ending in -st actually contains the -s of the genitive ending (which we still have today, though usually written as ’s, of course). In Middle English, this was often added to words used as adverbs (as while became whiles, which often turned up in the compound adverbs somewhiles and otherwhiles). What seems to have happened is that a -t was later added in the south of England through confusion with the superlative ending -st (as in gentlest).
Both while and whilst are ancient, though while is older. There’s no difference in meaning between them. For reasons that aren’t clear, whilst has survived in British English but has died out in the US. However, in Britain it is considered to be a more formal and literary word than its counterpart. I have a small weakness for it, for which I’ve been gently teased in the past.