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The philosopher Chaim Perelman distinguished what he called the "formal" and the "concrete" aspects of justice. The formal element was the rule that persons with the same "essential" characteristics should be treated equally. The concrete aspect was a particular specification of what the essential characteristics were. These essential characteristics are the same as the "relevant considerations" referred to in the dialog.
In Perelman's view, there had been many specifications for concrete justice. Various people had suggested that need, merit, work, rank, and race be considered essential characteristics. What all these specifications had in common was that each required that essentially similar people be treated in the same way.
In writing his introduction to Perelman's work, the legal philosopher H. L. A. Hart rephrased Perelman's views by saying that his distinction between essential and concrete "might be presented in terms used in recent English moral philosophy as one between the constant definition of justice and the varying criteria for its application in different situations or to different subject matters."
Reference: Chaim Perelman, The Idea of Justice and the Problem of Argument, translated by John Petrie, introduction by H. L. A. Hart.