When used to mean during the time that, at the same time as or although, the words whilst and while can be used interchangeably. If you want to play it safe though, use while. (More on this below.)
While or WhilstMost Americans find whilst quaint, old-fashioned, or literary. Most Brits, on the other hand, will swap happily between while and whilst, although some Brits also find whilst a little outdated.
Some grammarians engaged in the while-whilst debate claim that, in the meaning during the time that or at the same time as, whilst should be used for a short period of time, and while should be used for a longer period of time.
Building on this idea, some claim that whilst is like when, and while is like during. Some try to formalise this idea a little more, stating that while should be used with the past progressive tense. I'm not going to offer examples because these ideas are not well supported.
The bottom line is while and whilst are interchangeable (if you can live with the risk that some of your readers might find whilst a little pretentious).
Of course, while and whilst can also mean although. Some claim that, in this meaning, only while can be used. But, you will also hear it said that only whilst can be used in this role. Again, neither of these rules is well supported, and while and whilst are interchangeable in this meaning too.
The final advice: If you're unsure which to use, choose "while" (especially if you're an American).
While As a Noun or VerbWhile and whilst are not always interchangeable. They are only interchangeable when they are used as conjunctions (i.e., in the meanings outlined above). While can also be a noun or a verb. Whilst cannot. As a noun, while means a period of time. As a verb, it means to pass time (usually at a leisurely pace). For example:
IT'S DIFFERENT FOR AMERICANS, AUSTRALIANS, BRITS, AND CANADIANS
Canadians and Americans, use while unless you're trying to add a sense of the old fashioned.
Brits and Australians, use whichever one you want, but if you need to play it safe, use while unless you deliberately want to add a sense of the old fashioned.
What are conjunctions?
Among or amongst
List of easily confused words