The main conflict in both Oscar Castro Z's "Lucero" and Langston Hughes' "Thank You, M'am" exists because of the "inexorable, impartial voice" of fate. In "Lucero," Ruben Olmos fires a pistol at the same exact time another man does (in order to lay claim to pass a very narrow passage first). Unfortunately, Ruben loses a coin toss and must push his best friend (his horse, Lucero) off the side of the mountain. In this story, the protagonist faces both external (the other man passing on the cliff) and internal conflict (having to push Lucero off the mountain). In the same way that Ruben must face fate, so must Roger.
Roger does not have any idea that the woman he robs will not allow it. Fate brings the two of them together. In the end, Roger learns a huge lesson from Mrs. Luella Bates Washington Jones. Wanting blue suede shoes, Roger tries to steal the pocketbook of Mrs. Luella Bates Washington Jones. She does not allow this to happen. Roger, by the end of the story, faces both internal and external conflict. The external conflict he faces comes from his inability to escape from the half nelson Mrs. Luella Bates Washington Jones puts him into. Internally, Roger wants her to think well of him. He refuses to allow Mrs. Luella Bates Washington Jones to not trust him again (illustrated when he does not take money she leaves out).
As for the resolution of both stories, while Ruben and Roger both learn valuable lessons, Ruben comes away less of a man than when the story began, and Roger comes away more of a man.
The conflict in "Lucero" is that of person against fate wherein luck and chance determine the outcome of events and happiness for the characters along with a person against person conflict. The conflict in "Thank You, M'am" is one of person against person coupled with person against self. These two central kinds of conflicts do not compare as much as contrast. Perhaps the more interesting is "Thank You," in which the boy and the woman both face or have faced self against self conflicts and now also face a self against other conflict. In "Lucero," the character faces off against a coin and a challenger.