[mail system] c. 1500, "riders and horses posted at intervals," to provide direct and rapid communication of messages and letters from one place to another by relays, from post (n.2) on notion of riders and horses "posted" at intervals along a route. Probably formed on model of French poste in this sense (late 15c.).
The meaning "system for the conveyance of letters" is from 1660s; it is attested from 1590s in the sense of "vehicle used to convey mails;" 1670s as "a dispatch of letters from or to a place." As a newspaper name from 1680s.
1701, "pleasure carriage," from French chaise "chair" (15c.), dialectal variant of chaire (see chair (n.)) due to 15c.-16c. Parisian accent swapping of -r- and -s-, a habit often satirized by French writers. French chair and chaise then took respectively the senses of "high seat, throne, pulpit" and "chair, seat," but this was after chair had been borrowed into English in the older sense.
Originally a one-horse, two-wheeled carriage for two persons, later extended to other types of pleasure or travelling carriages. Chaise lounge (1800) is corruption of French chaise longue "long chair," the second word confused in English with lounge.
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Harper, D. (n.d.). Etymology of post-chaise. Online Etymology Dictionary. Retrieved $(datetime), from https://www.etymonline.com/word/post-chaise