Whilst and amongst are more formal ways to say while and among. I live in America and don't use those words, but like Madeline said they most likely use those in England. The meaning is the same, but whilst and amongst are just more formal.

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 can be a more formal variant of while. I'm not British, although I have lived in the UK, so maybe they have other meanings or uses for whilst but this is my experience with those words. Hope this helped.