As with many things in comic books, origin stories change all the time. By and large her origin has been she was sculpted in clay by Hippolyta, but given life by various means or Greek gods over the years. Wonder Woman is no exception to having her story changed over the +75 years she's existed.
Per Wikipedia, in her Golden Age origin:
Initially, Wonder Woman was an Amazon champion who wins the right to
return Steve Trevor – a United States intelligence officer whose plane
had crashed on the Amazons' isolated island homeland – to "Man's
World" and to fight crime and the evil of the Nazis.
During this period, Wonder Woman joined the Justice Society of America
as the team's secretary.
How very 1940s, eh? Doesn't get much better in her Silver Age adaptation:
The new origin story increased the character's Hellenic and
mythological roots: receiving the blessing of each deity in her crib,
Diana is destined to become "beautiful as Aphrodite, wise as Athena,
as strong as Hercules, and as swift as Hermes."
At the end of the 1960s, under the guidance of Mike Sekowsky, Wonder
Woman surrendered her powers in order to remain in Man's World rather
than accompany her fellow Amazons to another dimension. Wonder Woman
begins using the alias Diana Prince and opens a mod boutique. She
acquires a Chinese mentor named I Ching, who teaches Diana martial
arts and weapons skills. Using her fighting skill instead of her
powers, Diana engaged in adventures that encompassed a variety of
genres, from espionage to mythology. This phase of her story
was directly influenced by the British spy thriller The Avengers and
Diana Rigg's portrayal of Emma Peel.
She gets to go back to some of her roots in the Bronze Age version:
With a new decade arriving, DC president Jenette Kahn ordered a revamp
in Wonder Woman's appearance. Artist Milton Glaser, who also designed
the "bullet" logo adopted by DC in 1977, created a stylized "WW"
emblem that evoked and replaced the eagle in her bodice, and debuted
in 1982. The emblem in turn was incorporated by studio letterer
Todd Klein onto the monthly title's logo, which lasted for a year and
a half before being replaced by a version from Glaser's studio.
With sales of the title continuing to decline in 1985 (despite an
unpublished revamp that was solicited), the series was canceled and
ended in issue #329 (February 1986) written by Gerry Conway, depicting
Steve Trevor's marriage to Wonder Woman.
The Crisis on Infinite Earths cross-over of 1986 was designed and
written with the purpose of streamlining most of DC's characters into
one more-focused continuity and reinventing them for a new era, thus
Wonder Woman and Steve Trevor were declared to come from the Earth-Two
dimension, and along with all of their exploits, were erased from
history, so that a new Wonder Woman character, story and timeline
could take priority.
And then we get to several Modern Age adaptations, which you can read about in detail on the provided Wikipedia link as it's a bit too long for this format, but to sum up:
- She's been an ambassador from Themiscira charged with bringing peace to the world of man.
- Paradise Island was destroyed and the Amazons scattered, with Diana as an orphan in New York
- Even doing away with the clay figure origin by making her an actual demi-goddess as the offspring of Hippolyta and Zeus.
Her origin has undergone an even more complicated retcon with DC's Rebirth attempt at a universe-wide retcon.
As such, I wouldn't take anything you read about the actual Greek legends as something any writer for Wonder Woman in any incarnation stuck to, in part or in whole. Comic book origin stories and characters, even those based on actual myth, are still at the whim of the writer(s) to play with, expand upon, or even do away with entirely.