The central similarity that can be identified in terms of theme between these two excellent short stories would be that of relationships. Both stories present us with couples who are struggling or are encountering difficulties in their relationships, for different reasons. In "Cathedral," the narrator seems to present himself initially as a rather selfish, self-absorbed individual who only allows Robert, his wife's friend, to come and stay with them through emotional blackmail. As he reveals later on, it is clear that their marriage is struggling:
Every night I smoked dope and stayed up as long as I could before I fell asleep. My wife and I hardly ever went to bed at the same time. When I did go to sleep, I had these dreams.
Carver presents us with a relationship that is going through a very difficult period through the lack of communication and personal difficulties of the protagonist, but through the arrival of Robert and the relationship that he strikes up with the narrator, the reader is able to see the development of the protagonist that gives hope for the future.
In "Hills Like White Elephants," there is a similar presentation of a relationship that is going through some significant challenges. Through the comments of the American partner, it becomes clear that Jig is pregnant and he does not want her to keep it:
"It's really an awfully simple operation, Jig," the man said. "It's not really an operation at all... I know you wouldn't mind it Jig. It's realy not anything. It's just to let the air in."
The way Jig ignores these comments and tries to change the subject shows that she does not want an abortion. However, as the story develops, it becomes clear that she is being forced into having one in order to sustain their relationship. The crucial difference between these two tales and the theme of struggling relationships is that "Cathedral" ends on an optimistic note whereas there is no such hope for the couple in "Hills Like White Elephants."