On the other hand, one could certainly make the argument that these characters are static, meaning that they remain relatively unchanged in any significant way in the story. In the beginning, the qualities that define Jim and Della are their unselfish love for one another and their poverty, and, by the end of the story, these qualities still define them. They have realized that their wealth of love for each other is ultimately of more importance than their lack of funds, but their realization of this fact does nothing to change them in any significant way: the couple remains as committed to one another's happiness as they were to begin with. For this reason, I would argue that they are static characters who do have a realization, but the realization does not change them in any fundamental way.
Both characters, Della and Jim, in "The Gift of the Magi" are dynamic characters, defining a dynamic character as one who changes throughout the story. At the beginning of the story they both clearly feel that they can only prove their love to the other through extravagant gifts which neither of them can afford. Della ends up cutting and selling her hair to buy Jim a chain for his watch and Jim sells his watch to buy Della beautiful combs for her long hair. When Della presents Jim with his gift, and Jim sees that Della has cut off her hair to afford the watch chain, both characters realize that the gifts are unimportant and that it is the love that they feel for each other that is the best gift of all. Hence, both of the main characters would be considered dynamic.