while and whilst, conjunction mainly used in UK, can find their equivalents in AmE as during and although. whilst is much more formal. (Middle English whilest, alteration of whiles)
e.g.
While/whilst/although I accept that he's not perfect in many respects, I do actually quite like the man.
While/whilst/although I fully understand your point of view, I do also have some sympathy with Michael's.
I read it while/whilst/during the time you were drying your hair.
I thought I heard him come in while/whilst/during the time we were having dinner.