Titans, Gigantes and Demigods
Greek tradition holds a war of giants against the gods and a whole class of divine-human offspring.
The tradition
Hesiod's Theogony describes the Titans and their overthrow; the Gigantomachy pits earth-born Gigantes against the Olympians; heroes such as Herakles and Perseus are children of a god and a mortal woman. The Greek translators of the Hebrew Bible chose gigantes to render nephilim.
Why the translation choice matters
That single lexical decision in the Septuagint imported the Greek giant-mythology frame into every downstream translation, including English. Much of the popular 'giants' imagery descends from the word choice rather than the Hebrew.
The limit
Parallel does not equal identity. Greek demigods are heroic and often honoured; the Genesis account is a prelude to judgment. The moral shape of the stories differs even where the plot rhymes.