Typically, Brits use whilst and Americans use while. That's the main difference. When used as a conjunction or an adverb, while and whilst are interchangeable: There wasn't much Stanley could do while he waited.

Is Whilst past tense?

I was given to understand that "While" is the present tense and "Whilst" is the past tense. For example: "He sings while he is is in the shower." and "When he was alive, he sung whilst in the shower."

Which is older while or whilst?

'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.