"sleeveless cloak, circular covering for the shoulders," a Spanish style, late 16c., from French cape, from Spanish capa, from Late Latin cappa "hooded cloak" (see cap (n.), which is a doublet). Late Old English had capa, cæppe "cloak with a hood," directly from Late Latin.
"promontory, piece of land jutting into a sea or lake," late 14c., from Old French cap "cape; head," from Latin caput "headland, head" (from PIE root *kaput- "head"). The Cape of Good Hope at the southern tip of Africa has been the Cape since 1660s. Old sailors called low cloud banks that could be mistaken for landforms on the horizon Cape fly-away (1769).