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mid-14c., "morally discerning, prudent, circumspect," from Old French discret "discreet, sensible, intelligent, wise," from Latin discretus "separated, distinct," in Medieval Latin "discerning, careful," past participle of discernere "distinguish" (see discern). Meaning "separate, distinct" in English is late 14c.
Spellings discrete and nativized discreet co-existed until after c.1600, when discreet became the common word for "careful, prudent," and discrete was maintained in philosophy, medicine, music and other disciplines that remembered Latin and made effort to obey it. Related: Discreetly.