card (n.1)
c.1400, "playing card," from Middle French carte (14c.), from Latin charta "leaf of paper, tablet," from Greek khartes "layer of papyrus," probably from Egyptian. Form influenced after 14c. by Italian carta (see chart (n.)).

Sense of "playing cards" also is oldest in French. Sense in English extended by 1590s to similar small, flat, stiff bits of paper. Meaning "printed ornamental greetings for special occasions" is from 1869. Application to clever or original persons (1836, originally with an adjective, as in smart card) is from the playing-card sense, via expressions such as sure card "an expedient certain to attain an object" (c.1560).

Card table is from 1713. Card-sharper is 1859. House of cards in the figurative sense is from 1640s, first attested in Milton. To have a card up (one's) sleeve is 1898; to play the _______ card is from 1886, originally the Orange card, meaning "appeal to Northern Irish Protestant sentiment (for political advantage)."
card (v.1)
"to comb wool," late 14c., from card (n.2) or else from Old French carder, from Old Provençal cardar "to card," from Vulgar Latin *caritare, from Latin carrere "to clean or comb with a card," perhaps from PIE root *kars- "to scrape" (see harsh). Related: Carded; carding.
card (v.2)
1540s, "to play cards" (now obsolete), from card (n.1). From 1925 as "to write (something) on a card for filing." Meaning "require (someone) to show ID" is from 1970s. Related: Carded; carding.
card (n.2)
"machine for combing," late 14c. (mid-14c. in surname Cardmaker), from Old French carde "card, teasel," from Old Provençal cardo or some other Romanic source (compare Spanish and Italian carda "thistle, tease, card," back-formation from cardar "to card" (see card (v.1)). The English word probably also comes via Anglo-Latin cardo, from Medieval Latin carda "a teasel," from Latin carduus.