William Kitchiner M.D. (1775–1827) was
an optician, inventor of telescopes,
amateur musician and exceptional cook.
His name was a household word during
the 19th century, and his Cook’s
Oracle was a bestseller in England
and America.
Wikipedia
The phrase forty winks, meaning a short nap, can be traced back to Dr. Kitchiner's 1821 self-help guide, The Art of Invigorating and Prolonging Life. The phrase is mentioned in a November 1821 issue of the British Literary Chronicle, in a review of Kitchiner's book:
Sleep is a subject on which our author
acknowledges his feelings are
tremblingly alive; he is fond of a
'forty-winks' nap in an horizontal
posture,' as the best preparative for
any extraordinary exertion, either of
body or mind.
Here is a clip from an 1822 copy of Kitchiner's book:
The use of quotes around a forty winks nap seems to indicate Kitchiner might have borrowed the phrase from elsewhere, but I can't find it in any form earlier than his use of it. Also, Kitchiner carefully footnotes other phrases and passages from different authors throughout his book.
Could the BE slang term ‘kip’ meaning to sleep be a borrowing from Hokkien? I searched Hobson/Jobson and came up with this:
CHOP-CHOP . Pigeon-English (or -Chinese) for 'Make haste! look sharp!' This is supposed to be from the Cantonese, pron. kăp-kăp, of what is in the Mandarin dialect kip-kip. In the Northern dialects kwai-kwai, 'quick-quick' is more usual (Bishop Moule). [Mr. Skeat compares the Malay chepat-chepat, 'quick-quick.']
The characters here, as Janus suggested, are most likely 急急. Hobson-Jobson is clearly mistaken in referring to ‘kip-kip’ as Mandarin rather than Hokkien. This entry might be read as saying that ‘chop-chop’ and ‘kip-kip’ were competing forms donated by different Chinese dialects/languages. However, it’s not clear if the latter was ever used in English or not.
In any case, if English had already borrowed a version of this Chinese word to mean ‘quick’ with no semantic shift, why would it re-borrow the same word from a different dialect to mean ‘sleep’? It seems highly unlikely. Generally, to establish a relationship of borrowing we would want to have three things: (A) a phonetic link, (B) a semantic link and (C) a context (a time and place where the donor and recipient languages would have been in contact.)
With ‘kip’ we have A, it seems, but even that could be challenged. Initial ‘k’ represents an aspirated stop in both English and pinyin, but in other Chinese dialects it might well be pronounced without aspiration and thus sound more like an English ‘g’. And how did Cantonese ‘gap’ become English ‘chop’? Sound change in borrowed words can be idiosyncratic.
Concerning B, any semantic link between ‘quick’ and ‘sleep’ would be forced. Did Chinese people in a 19th century treaty port who wanted to take a nap after lunch ever say ‘kip-kip’ to signify ‘just a short one’ to English people, who then misinterpreted the word to mean sleep? It seems too tenuous to take seriously.
Finally C, the context. Where would the hypothetical encounter in B have taken place, and at what point in time? The history of Chinese-Western contact is of course very complex. We might be talking about the south China coast in the 19th century. The main treaty ports frequented by English traders, at least before the country was ‘opened up’ after the 1840 Opium War, were Canton and Hong Kong. Since these are located in a Cantonese-speaking area, it’s probably safe to take Cantonese as the default donor language for loans into British English. However, other points of contact like Singapore would have had a different mix of dialect groups – generally for Southeast Asia the Hokkien communities were larger and more numerous than Cantonese ones, so the contact language might have been Hokkien. And so on.
The formal title of Hobson/Jobson is ‘Glossary of Anglo-Indian Words and Phrases…’, but it actually covers ‘Oriental terms’ more broadly, not just South Asian ones. More about this dictionary here:
Hobson-Jobson definitively
TL/DR: No, ‘kip’ wasn’t borrowed from Chinese.
Best Answer
Nap and 40 Winks, at least, are interchangeable synonyms, both meaning a short period of sleep, with a special emphasis on those periods occurring during the day, or at least at a time other than when one is supposed to be sleeping (or turning in for the night, for the cultural meaning of 'the daily period of sleep at the end of the day').
So one could conceivably nap the entire afternoon away for a period of 4 hours, but at the same time one could turn in for the night at 2 am and get up and 6, and we wouldn't call it a Nap.
Definitions for both from the Merriam-Webster:
A Power nap is an expression coined by Cornell University social psychologist James Maas. It refers specifically to a short sleep of 20 (or sometimes 30) minutes or less which ends before the occurrence of deep or 'slow-wave' sleep.
Snooze is fairly interchangeable with the above words, but it introduces an element of lightness to the rest.
Kip seems to be a chiefly British word that's a lot more versatile. It may be the 'Britishness' of it that makes it feel 'old-fashioned' to non-British speakers, perhaps. And while it can be used to mean a nap, it can also refer to nightly turn in.
As can be seen from the examples, kip is more interchangeable with sleep than nap. One can have a short kip or kip down for the night.
Siesta is a lot more specialized, though. One could siesta in winter, but you couldn't at 10 am in the morning or 5 pm in the evening. It specifically refers to a period of sleep in the afternoon, almost always post-lunch.
The special reference to certain countries and climates comes because in many of those countries, those post-lunch hours are (/were pre-air conditioning) too hot to do anything. So siestas are a culturally significant period of time, during which shops might be closed and schools might get out early during 'siesta time' in the summers.
Dates regarding etymology:
Nap: Possibly the oldest one here. From Old English hnappian "to doze, sleep lightly". In use from c. 1300, and in the construction "take [] nap" c. 1400.
40 Winks: Dr. Kitchiner, The Art of Invigorating and Prolonging Life (1821) Link
Power Nap: Maas, James B.; Wherry, Megan L. (1998). Miracle Sleep Cure: The Key to a Long Life of Peak Performance Link
Snooze: First used in 1789. The meaning "a short nap" is from 1793. Etymology seems to onomatopoeia referring to a snore.
Kip: Seems to have originated in around 1760s from the Danish word kippe (a hut or a mean alehouse) -> Irish slang term for a brothel (Earliest example in Oliver Goldsmith’s The Vicar of Wakefield (1761)) -> British slang for common lodging-house for tramps and the homeless (c. late 19th century) -> to the act of sleeping itself. The the modern informal or colloquial usage seems to have started in the twentieth century itself. Link
Siesta: The second oldest English word from 1650s, borrowed from the Spanish word siesta, from Latin sexta (hora) "sixth (hour); But its etymology might be the earliest thanks to the Latin root.