Old Persian magush, Babylonian magush, Greek magos: the Magi were the priestly caste of the Iranian west, attested from Darius's Bisitun inscription, where the usurper Gaumata is named a magu. Herodotus makes them a Median tribe of dream-interpreters and sacrifice-masters; no Persian sacrifice was valid without one chanting the theogony. Greek turned their craft, astrology, dream-reading, ritual, into mageia, the stuff magoi do, and Latin magia gave English magic. The Magi of Matthew's gospel are the same word.
Scholars like Gershevitch argue the Magi were originally technicians for hire, professional priests serving any cult, who adopted Zoroaster late and wrote themselves into his story, and whose dualism, Oromasdes versus Areimanios, Aristotle reported as their doctrine. The Greeks could never decide whether Persian magi were profound sages or Babylonian imposters, so the word carried both charges at once, which it still does: magic means wonder and fraud simultaneously, the only word that is its own debunking.
The claim: mageia never meant the supernatural, it meant the neighbor's religion, rites whose authority the Greeks could not verify and therefore classed as power-tricks; magic is what your rival calls your liturgy when his gods are not listening. Verdict: supported by the usage history, the word degrades as it travels from one empire's priests to another empire's storytellers. Every age since has repeated the move: technology you cannot inspect is magic, liturgy you cannot join is magic, and the magush's heirs are still chanting, now in server rooms.
If magic means what the Magi did, what exactly did the Magi do?