Abarim Publications' online Biblical Greek Dictionary
αετος
The noun αετος (aetos) generally means raptor and describes any large carnivorous flying bird: eagles, vultures, buzzards. It relates to the familiar Latin avis (from which English gets avian), which describes any bird in general, and stems from the Proto-Indo-European "hewis", bird. Both words are suspiciously similar to the Latin ovis, sheep, which may suggest that both were named from a verb that described apparel and dress. That would mean that to the Greeks, an eagle was basically a big bird, and a bird was predominantly known for its fancy feathers and flamboyance.
But these words may also essentially share a root with the familiar Latin noun ovum, egg, and identify birds essentially as egg-layers. That would relate birds rather spectacularly to snakes and crocodiles, and this in turn would explain the kinship of the imagery associated with angels (winged spirits) and demons (snake-like snarlers). The ancients doubtlessly observed that all mammals, including humans, gestate within their mothers' bodies, and after birth drink milk that is produced by those same bodies (1 Corinthians 3:2). Egg-beings, on the other hand, gestate in little concrete cells, whose lifeless walls must be overcome by force from the inside out. And upon birth, egg-creatures immediately eat what adults eat. Then suddenly, they spread their wings and take flight.
Societies in antiquity usually highly valued their bird-people. Modern ones not so much.
Stories like that of Noah and Gilgamesh suggest that the ancients figured that the whole of the human mental cosmos is a fractal equal of the whole of the biosphere — like Michelangelo's Creator-making-Adam, the whole of Noah's ark is within man's head — meaning that our modern human reality is rather like a farm, governed by shepherd-people, driven by dog-people and peopled mostly by herd-people. Wildlings are rare in our modern world, but reptiles and birds exist in abundance.
Birds see further and react to a much greater range than a dog or a shepherd can imagine to exist (Ecclesiastes 10:20, Hebrews 12:1). Dogs don't understand this (dogs have no Theory of Mind to speak of) but shepherds do. This is why a shepherd looks at birds and tries to read their behavior, and interprets their behavior for information about what's going on in the wider area around them (Exodus 19:4, Deuteronomy 32:11-12, Psalm 103:5, Isaiah 40:31). Birds know where the herds are, where the water is, where large and undomesticated predators prowl. Birds know the weather before it comes, where fruits ripens, what time of year it is.
Shepherd-people read birds like books (Matthew 6:26, Job 9:26). Dog- and herd-people imagine that there's magic involved and look at birds for omens. Zeus kept a huge eagle/vulture by his side, but that's probably because eagles hunt rodents (petty criminals that burrow in river banks and destabilize the surface world) and vultures circle the dead and dying (schools of thought that coast on ancient momentum rather than actual intellectual support; once dead these carcasses first attract proper robbers, but then quickly flies and such horrors).
The noun αετος (aetos), eagle or vulture, is used 5 times; see full concordance. The Latin equivalent of this noun is aquila, which is also the name of an important early adopter of the Gospel: Aquila, whose name occurs an additional six times in the New Testament.