What is the difference between while and whilst?

In American English whilst is not normally used. In British English while and whilst are more or less interchangeable when the meaning is although or whereas.

Whilst many people agree that boxing is dangerous, little has been done so far to ban it.

It will remain cold in the west, eastern areas should be noticeably milder.

In the meaning of when, whilst is significantly more formal and may appear archaic. Compare:

I first met her while I was working for a company in the Midlands.

I first met her whilst working for a company in the Midlands.

Similarly amongst and amidst are more formal and literary than among and amid, although in one or two phrases, for example amongst others, they may occur quite frequently. Incidentally, one American source dismisses these as “Briticisms or archaisms”.

While Or Whilst

I have noticed that in the UK people often use the word 'whilst'--we rarely use that here in the USA.

The British prefer whilst while here in the US while is the norm.

In a while - later on

Whilst I was doing something.

Whilst is basically the British version of while. They both mean the same thing.

They mean the same, and are both in use in the UK. "While" is the more modern.

there is not difference. It's just the era of time it was used.

it's somewhat like ye and you.