The basic similarity in these three stories by O. Henry is their surprise endings, which is an O. Henry trademark.
In "After Twenty Years," "Silky" Bob discovers that the policeman he had been talking to in the doorway of the hardware store was actually his old friend Jimmy Wells and that Jimmy had to have him arrested because it was his duty. In "The Last Leaf" it is discovered that the leaf which seemed to cling so tenaciously to the vine had been painted there by a man who sacrificed his own life to save that of the girl who had expected to die when that leaf finally blew away. And in "Tobin's Palm," Tobin discovers that the man with the crooked nose whom the fortune teller had told him would bring him good fortune was actually the man who, rather than bringing him money, would bring him together with his lost love Katie Mahorner.
Other similarities are the misapprehensions involved in all three stories and the affection between characters in all three.