The Ancient Greek word "daimon" doesn't mean "demon".
Daimon or Daemon (Ancient Greek: δαίμων, "god", "godlike", "power", "fate") originally referred to a lesser deity or guiding spirit such as the daimons of ancient Greek religion and mythology and of later Hellenistic religion and philosophy. The word is derived from Proto-Indo-European daimon "provider, divider (of fortunes or destinies)," from the root da- "to divide".
Daimon or Daemon (Ancient Greek: δαίμων, "god", "godlike", "power", "fate") originally referred to a lesser deity or guiding spirit such as the daimons of ancient Greek religion and mythology and of later Hellenistic religion and philosophy. The word is derived from Proto-Indo-European daimon "provider, divider (of fortunes or destinies)," from the root da- "to divide".
-- Wikipedia (https://en.wikipedia.org/wiki/Daimon)
The sorts of beings modern English refers to as "demons" are* daimons, but so are "guardian angels" and "saints".