But there are, of course, some similarities. Here are two photos. The first is from a production of Jean Racine's "Phedre," which directly dramatizes the myth. The second is from a production of "Desire under the Elms."

The Phaedra-Hippolytus relationship ends much more catastrophically than the Abbie-Eben relationship - both the mythological characters die, she by poison, he by being trampled in his own runaway chariot. And, crucially, Hippolytus never feels anything for Phaedra but dislike or revulsion; Eben feels the same at first, but his feelings change over the course of the play. But the physical situations in these pictures are strikingly similar, despite the plot differences. The trapped woman who still exerts sexual influence, the young man unable to take definite action without her prompting, the intense physicality of the scenes, and the danger of giving in to those physical impulses that drive the relationships - these are constants of both plays, and come across equally strongly in these pictures.
And how about the woman and her husband? Cabot is very much Abbie's senior - part of her dilemma stems from the fact that he's probably not going to get her pregnant. In the myth, on the other hand, there's no reason to believe that Theseus is vastly older than Phaedra - after all, he was once engaged to her sister Ariadne. Here's a photograph (from the same production of "Desire") of Cabot and Abbie:
And here's a photograph of Phaedra and Theseus from a "Phaedra" production:
Eerily similar! A notably older man, a younger (if not "young") wife who can't hide her disgust - DESPITE the reason that in "Phaedra," there's no textual need to make Theseus this old. O'Neill was on to something with the age difference between Cabot and Abbie - not only does it help to explain Abbie's attraction to Eben, but it widens the gap between Abbie and Cabot to a chasm that cannot be crossed.
There's more going on here than an adapted story. O'Neill fixed on the heart of the characters' relationships. Because they translate so effortlessly from Greek tragedy to 20th-century drama, they end up feeling timeless - disturbingly so, since not a single relationship escapes havoc and chaos and heartbreak. But then again, what else is tragedy about?