[This entry is taken from a chapter of Part II of the open-source textbook Spanish-English Cognates: An Unconventional Introduction to Spanish Linguistics.]
Sp. servilleta ~ Eng. serviette
Sp. servilleta [seɾ.βi.ˈʎe.t̪a] means ‘napkin’. English has a cognate of this word, namely serviette, which is just a fancy word for ‘napkin’, used primarily in Great Britain. The OED tells us that English borrowed this word in the late 15th century from the identical French word serviette that meant ‘a towel, table-napkin’, though early on it was spelled in different ways, such as serviot or serviat (OED). Actually, it seems that original serviette was only used in the Scottish dialect of English and that standard English reborrowed this word from French in the 19th century with the French spelling. Today, Eng. serviette is pronounced [səɹ.vɪ.ˈɛt] or [ˌsɜɹ.vɪ.ˈɛt].
The main meaning of Eng. serviette from the very beginning has been ‘a cloth, usually of linen or hemp, for wiping something dry, esp. for wiping the hands, face, or person after washing or bathing. Also formerly more widely, including a table-napkin or other cloth used at meals’ (OED). Merriam-Websters Collegiate tells us that it is a ‘chiefly British’ word for ‘table napkin’. The Oxford American Dictionary tells us that it is a British and Canadian word for ‘table napkin’. Chambers tells us that it means ‘a table-napkin, especially a paper one’, a fact mentioned by very few other dictionaries (another one is the Shorter Oxford English Dictionary).
The exact source of French serviette, pronounced [sɛʀˈvjɛt], is not clear. The OED says that it is ‘of obscure formation’, though the ending of the French word clearly identifies it as a diminutive word and there is no doubt either that this word is ‘connected with the verb servir’ (OED). French etymological dictionaries tell us that Fr. serviette was first attested in 1328 (LGR) or 1361 (TLFi) and that it comes from servir. According to TLFi, this word is derived from servir by means of the suffix ‑iette, a variant of the diminutive ‑ette suffix, and that it came to replace the French word touaille, cognate of Sp. toalla and Eng. towel, all descendants from West Germanic *þwahljô (Kluge) (OED), derived from Proto-Germanic *þwahaną ‘to wash’, cf. Frankish *þwahilu ‘cloth’. Thus, there is no cognate of Eng. towel ~ Sp. toalla in Modern French today, since this word has been replaced by serviette (de toilette). Another word for a hand towel is essuie-mains, a compound formed with a form the verb essuyer ‘to wipe’ and the word mains ‘hands’ (from Latin exsūcāre ‘lit. to juice out; to dry’ (cf. rare Sp. enjugar ‘to wipe away’).
Sp. servilleta is first attested in the second half of the 16th century, though the spelling servieta is also attested. DCEH tells us that it was ‘probably taken from Fr. serviette’, though there is little doubt that this is the source of the Spanish word. Note that it was quite common to adapt borrowed diminutive French words in ‑ette with the ending ‑eta, a cognate of the Spanish diminutive suffix ‑ita, e.g. bicicleta (late 19th century), from Fr. bicyclette, itself a diminutive of bicycle, borrowed from English, and croqueta ‘croquette’, from Fr. croquette, a diminutive word derived from the verb croquer ‘to crunch’.
As we can see, Eng. serviette is a synonym of the word napkin, though the former is much more common in Britain than in North America. Spanish only has one word to translate both English words, namely servilleta.
Eng. napkin has come to be used with extended meaning in North America, namely as an ellipsis of the phrase sanitary napkin, which is another way to refer to a sanitary towel or sanitary pad in North America. All these terms refer to ‘a thick band of soft material that women put inside their underwear during menstruation’ (Macmillan).
The most common way to refer to sanitary towels in Spanish is by means of the calque toalla sanitaria, even though it does not refer to a towel, strictly speaking. However, some dialects of Spanish have calqued the North American expression sanitary napkin as servilleta sanitaria, even though it does not refer to a napkin strictly speaking either.
Common phrases that include the Spanish word servilleta are servilleta de un solo uso and servilleta de usar y tirar, both of which mean ‘disposable napkin’, and servilleta de papel ‘paper napkin, (British) paper serviette’.
 Eng. napkin is derived (in English?) from the Old French nape or nappe that meant ‘tablecloth’ by means of the diminutive suffix ‑kin, e.g. s catkin, lambkin, manikin (cf. mannequin), ‘from or after Middle Dutch ‑kijn, ‑ken, German ‑chen, as in Middle Dutch husekijn, huusken, German Häuschen little house’ (SOED). Eng. napkin can also be used in British English with the meaning ‘diaper’, though that sense is now dated (COED). An alteration of napkin with just that sense is nappy. Note that his word is unrelated to the ‘U.S. slang (frequently derogatory)’ adjective nappy that means ‘frizzy’ or ‘kinky’ referring to ‘a black person's hair’ (COED),. This word was presumably related to Middle Dutch noppich (Dutch noppig; cf. Middle Low German noppich) and also related to Eng. nap ‘a soft or fuzzy surface on fabric or leather’ (AHD), probably borrowed form Middle Dutch nop or noppe, though the form of this nap may have been influenced by the word nape that was borrowed from French and is the source of napkin (AHD).