demon (n.)youdaoicibaDictYouDict[demon 词源字典]
c. 1200, from Latin daemon "spirit," from Greek daimon "deity, divine power; lesser god; guiding spirit, tutelary deity" (sometimes including souls of the dead); "one's genius, lot, or fortune;" from PIE *dai-mon- "divider, provider" (of fortunes or destinies), from root *da- "to divide" (see tide (n.)).

Used (with daimonion) in Christian Greek translations and Vulgate for "god of the heathen" and "unclean spirit." Jewish authors earlier had employed the Greek word in this sense, using it to render shedim "lords, idols" in the Septuagint, and Matt. viii:31 has daimones, translated as deofol in Old English, feend or deuil in Middle English. Another Old English word for this was hellcniht, literally "hell-knight."

The original mythological sense is sometimes written daemon for purposes of distinction. The Demon of Socrates was a daimonion, a "divine principle or inward oracle." His accusers, and later the Church Fathers, however, represented this otherwise. The Demon Star (1895) is Algol.[demon etymology, demon origin, 英语词源]
fate (n.)youdaoicibaDictYouDict
late 14c., "one's lot or destiny; predetermined course of life;" also "one's guiding spirit," from Old French fateand directly from Latin fata (source also of Spanish hado, Portuguese fado, Italian fato), neuter plural of fatum "prophetic declaration of what must be, oracle, prediction," thus the Latin word's usual sense, "that which is ordained, destiny, fate," literally "thing spoken (by the gods)," from neuter past participle of fari "to speak," from PIE *bha- (2) "speak" (see fame (n.)).

From early 15c. as "power that rules destinies, agency which predetermines events; supernatural predetermination;" also "destiny personified." Meaning "that which must be" is from 1660s; sense of "final event" is from 1768. The Latin sense evolution is from "sentence of the Gods" (Greek theosphaton) to "lot, portion" (Greek moira, personified as a goddess in Homer). The sense "one of the three goddesses (Clotho, Lachesis, and Atropos) who determined the course of a human life" is in English by 1580s. Often in a bad sense in Latin: "bad luck, ill fortune; mishap, ruin; a pest or plague." The native word in English was wyrd (see weird).