"Just us" vs. justice is new to me. It seems the distinction may be whether justice is warranted. If not, it's "just us."
Justice is defined as...
...the administering of deserved punishment or reward.
Oedipus did not kill his father and marry his mother knowingly, but he is held accountable by the "gods." When Thebes experiences loss of harvest, animals and outbreak of disease, the people look to Oedipus to find the cause. He seeks word from the oracle at Delphi. Creon reports that tragedy plagues Thebes because of the murder of Thebes' former king, Laius; and the murderer must pay—justice must be served:
[Laius] fell; and now the god's command is plain:
Punish his takers-off, whoe'er they be.
Unfortunately, the murderer is Oedipus. Oedipus took a stranger's life—that of his father—and Laius brought the fight upon himself. Oedipus saved Thebes by solving the Riddle of the Sphinx, and married Jocasta (his mother) at the urging of the people of Thebes. However, regardless of his unintentional culpability, justice is required of him. And in mythology, one is generally punished.
In Chopin's " Désirée's Baby," there is a need for justice, but no payment. Désirée (an orphan) marries and gives birth her first child: a baby boy. Though formerly harsh on the plantation's slaves, her husband's love for his wife and child change him—until the child is a couple of months old. It becomes obvious then that the baby is part black, and Armand becomes like "the very spirit of Satan." He avoids his family. When Désirée confronts Armand, he insists that she and the child leave.
In her portrayal of Désirée, a woman['s] self-worth and self-exploration is intrinsically linked to that of her husband,
Devastated by his rejection, Désirée takes her child, and instead of going to her mother, she wanders into the bayou, where she and her child perish. Justice is not demanded of her—she is blameless. Armand is the monster, but he goes unpunished. An awful irony is revealed at the end as he burns all that belonged to wife and child, including letters from her, and one more:
…it was part of an old letter from his mother to his father. He read it. She was thanking God for the blessing of her husband's love:--
"But above all," she wrote, "night and day, I thank the good God for having so arranged our lives that our dear Armand will never know that his mother, who adores him, belongs to the race that is cursed with the brand of slavery."
Armand is responsible for the child's ancestry; he is to blame for his racism—his hatred for his slaves and his rejection of Désirée and their baby—but justice is not served.
Langston Hughes' "Suicide Note" is brief, but particularly poignant. After the Harlem Renaissance ended with the onset of the Great Depression, Hughes went on to write poetry that painted a "unremittingly bleak portrait" of life in the ghetto. Perhaps "Suicide Note" is a result. The cool water offers peace, and the subject of the poem leans in for a kiss—drowning. There is no need for justice.
Justice, then, refers to a person deserving punishment, though it may or may not take place. "Just us" speaks to people who are not victimized in some way, where justice is not required. Oedipus receives justice, though his sins were committed unknowingly. Armand deserves justice and receives none. In Hughes' poem, there is no punishment required: no justice...just us.