We are firmly in the thorny territory of the separation of American English from British English here, along with shifts in usage over time.
INCORRECT
- Would you make me a cup of tea whilst you are in the kitchen?
- I hope to plant lavender amongst the roses in the garden.
- Don’t laugh whilst eating; you might choke.
CORRECT
The examples above are “wrong” to American ears. Instead, make me a cup of tea while you are in the kitchen and plant your lavender among the roses. Americans tend to view amongst and whilst as charming (or fussy, depending on their outlook) hallmarks of British English. Speakers of British English (and some older Americans in the southern mountains) mostly use them interchangeably. Words such as amongst, whilst, and towards are called adverbial genitives; they are genitive-case nouns that function as adverbs. We use once, always, afterwards, hence, and others all the time. They are just as old as thrice and thence, but we use them more often, so they feel normal.
MORE TO KNOW
Languages evolve in fits and starts, depending on word usage by powerful people, as well as in literature. If you read British children’s books, the “incorrect” examples of whilst and amongst seem normal. Even among (ha!) speakers of British English, the use of among is far greater than the use of amongst. Amongst appears to be on its way out.