In both stories, the characters originally meet at the "sea-front," as Anton Chekhov puts it in "The Lady with the Dog." Anna, from Joyce Carol Oates version, meets the gentleman at Nantucket, Massachusettes, whereas Anton Chekhov''s Anna meets Gurov at Yalta, Russia. For Oates's Anna the setting changes to Albany, New York and to a concert and a hotel room. For Chekhov's Anna the scene changes to her home and to Moscow and a hotel room.
First, the settings affect the Anna's by giving them a sense of liberty, no matter how infinitesimally small--a liberty in being away from their husbands who have disappointed them. Then, the changes in scene affect the Anna's with a sense if isolation and despair that leads to eventually desperate yearning. Finally the changes in scene lead to new paths taken in life.
For Oates' Anna, the new path gives her full liberation as she commits her heart to the ideal of a marriage of hearts. For Chekhov's Anna, the new path leads to more difficulties as she is committing herself to either a life of continued despair or a life isolated from all association with society, provided Gurov can actually think of "How? How?...How?" which seems doubtful.