While and whilst can nowadays legitimately be used in the contrastive sense of although or whereas, provided that it is not ambiguous (although some commentators, such as Eric Partridge, have frowned upon such use):
This sentence can mean either "During the time that Sally plays, Sue works" or "Although Sally plays, Sue works".
Fowler's Modern English Usage disapproves of several uses of "while". At times it is inappropriately used as a conjunctive: actual conjunctions such as "and" should be used instead. Its usage as "elegant variation" is also discouraged, as it is masquerading as a "formal word".
Whilst is chiefly used in British English and Australian English. Whilst is synonymous with while in standard English, although to many it sounds slightly old-fashioned, and is rare or archaic. In their style guides, some modern publications on both sides of the Atlantic disapprove of its use (along with "amidst" and "amongst"), for example: