The earliest substantial account of the phoenix in Greek is also the most careful about its own limits.
Herodotus, writing in the fifth century BCE, describes in his second book a sacred bird called the phoinix which the Egyptians say visits Heliopolis once every five hundred years, when its parent dies. He reports that it comes from Arabia, encases the body of its parent in a ball of myrrh, and carries it to the temple of the sun. He notes the size and colouring he was given, comparing it to an eagle with red and gold plumage. And then he says, in terms, that he has not seen it himself and that he does not find the account of the myrrh convincing.
There is no burning in Herodotus. There are no ashes. The bird does not die by fire and is not reborn from its own remains. What it does is transport a corpse.
Behind the Greek report stands an Egyptian bird that is not quite the same thing. The bennu is a heron associated with the sun god at Heliopolis and with the primeval mound, and it functions in Egyptian theology as a manifestation of periodic renewal and of the sun's daily return. It has its own liturgy and its own iconography and it does not burn either. Its name is connected in Egyptian sources with a verb of rising or shining, and it is linked to the first land emerging from the waters of chaos and to the cycles by which time was reckoned, which is a theology of recurrence rather than of resurrection.
The Greeks appear to have heard about the bennu and its cycles and produced the phoinix, which is a Greek account of an Egyptian thing rather than a translation of it. The Greek word itself is unhelpfully overloaded, since phoinix also means the colour purple-red, the date palm, and a Phoenician, and ancient writers played on all of these; which sense generated which is not settled.