This is a very interesting question to consider. I suppose one of the major thematic links we could establish between the two texts is that of the search for identity.
Let us consider the captain in "The Secret Sharer" to begin with. It is clear that the story focuses on his own development and maturity as he faces the realities of the role and responsibility of his position. He is constantly looking for some sign that he is doing the right thing from his crew. Of course, a major influence on his process of growing into the role of captain is his friendship with Leggat, who teaches him that he must be more direct and aggressive to be a good leader. We see that in the story the captain is exploring and experimenting with different ways through which he can define himself.
Similarly, Paul is trying to establish his own identity, even if the identity he wants to establish is based on fiction rather than fact. Even though Paul emerges from a middle-class background, which is said to be "perfectly respectable, Paul sees the lives that his parents lead as boring and meaningless. He desperately wants to be rich and worry-free. Note how he refers to his home neighbourhood as he returns there:
Paul never went up Cordelia Street without a shudder of loathing. His home was next to the house of the Cumberland minister. He approached it tonight with the nerveless sense of defeat, the hopless feeling of sinking back forever into ugliness and commonness that he had always had when he came home. The moment he turned into Cordelia Street he felt the waters close above his head.
The way in which Paul describes his home clearly indicates his attempt to define himself in opposition to his roots, even if such attempts are based on fantasy. His visits to the opera show themselves to be nothing more than escapism, and Paul is able to achieve his goal, but only for one week, as he ventures out to New York to acheive the ultimate escape. Paul's week in the Waldorf Hotel and his enjoyment of the luxury that surround him reinforce Paul's impression that "money was everything." We are significantly told that Paul's "surroundings explained him." However, tragically, Paul is so fixated on this false identity that when the game is up and his escapism is due to end, he is unable to return to real life, and kills himself.