Hebrew malakh means messenger, used 124 times for divine envoys and 88 times for ordinary human couriers in the Hebrew Bible. Greek angelos is the same word, and the Septuagint used it to render malakh. Augustine formalized it: spirit by nature, angel by function. Biblical messengers look like men, walk, eat, and are regularly mistaken for travelers. Nowhere does a messenger-angel have wings; wings belong to cherubim and seraphim, beings never sent on errands.
Ancient Near Eastern gods and guardians, the winged lamassu of Assyria, the winged genii of Persia, put wings on anything holy long before Israel wrote a word. Greco-Roman Victory and Eros supplied the body plan for Christian art, and by the fourth century the winged humanoid was standard iconography. The Torah's messengers stayed wingless; the frescoes didn't. One art tradition overwrote a thousand pages of text in the public imagination.
The claim: Jewish angelology, named angels, ranks, a cosmic adversary, resurrection, judgment, was substantially assembled during and after the Babylonian exile under Persian influence, since pre-exilic texts have almost none of it and post-exilic texts have all of it. Verdict: the timing correlation is real and mainstream scholarship takes the influence thesis seriously, with the Jerusalem Talmud noting angel names became common after the return from Babylon. Correlation is not a download, though. The strongest version, angels are rebranded yazatas, overclaims; the sober version, exile taught monotheism a court vocabulary, is hard to dismiss.
If angel is a job description, what is the creature under the job?