while, whilst
1. Both forms are used in BrE, but whilst is not much used in AmE. There is no distinction in usage as regards meaning, although varying grammatical patterns are noted below.
2. The word is a conjunction, and its primary sense is temporal, meaning ‘during the time that’ (They had begun drinking while he prepared to cook) or ‘at the same time as’ (She enjoyed drawing while she was being read to). Since the time of Shakespeare, however, other uses have emerged in which while (or whilst) means ‘although’ or ‘whereas’, with concessive or contrastive rather than temporal force (While I enjoy his company, I couldn't live with him / I live in London, while my sister lives in New York). The concessive use (in particular) has been disapproved of by some (including Eric Partridge in Usage and Abusage, 1942 and later), but it is so well established that criticism is futile. Instances of possible ambiguity between the temporal and concessive–contrastive types of meaning are sometimes adduced, but they are usually contrived and unlikely to arise in practice (such as the old chestnut The Curate read the First Lesson while the Rector read the Second). Examples: (temporal)

• Here father and daughter sat side by side on the window seat while he coached her each evening in the school holidays —C. Brayfield, 1990

• (concessive) While domestic happiness is an admirable ideal, it is not easy to come by —T. Tanner, 1986

• While this division does not correspond exactly to Kant's division of chapters …, it is sufficiently close not to be misleading —R. Scruton, 2001

• (contrastive) Whilst Mackenzie carried on and ended up editing the Sun, Sutton began to question what he was doing —C. Horrie et al., 1988

• They practise in the town, with Champion cycling the streets to the peep of Gran's whistle, while Bruno spends the evenings climbing up and down stairs to bark at the trains —film website, BrE 2002 [OEC].

3. While and whilst are used elliptically, with the omission of a subject and main verb such as they were (in the first example following) or he was (in the second):

• Dinner ladies helping with playground supervision have been jostled and abused while trying to tackle unruly pupils —Daily Telegraph, 1983

• While still working for the restaurant in 1956, he began his franchising career —Money, 1985.

In this type of construction while (or whilst) is usually temporal (as in both of these examples) or concessive (as in the following example), and when concessive it tends to come before the main clause:

• More recent evidence, whilst not addressing this issue directly, tends to suggest that this desired relationship is still important —J. Finch, 1989.

4. A sentence such as the following is incorrect: ☒ While being in agreement on most issues, I would like to challenge one in particular. The omission is misconceived since the full form is while I am and not while I am being; correct while being to while I am in agreement or while in agreement.

Modern English usage. 2014.