Justice is justice. Your distinction is not true in Plato or Aristotle. And Aristotle was a teacher, not an aristocrat.
No, justice is not justice.
That statement has no context or meaing.
Socrates spent several chapters in the Republic with his interlocutors trying to define justice.
Social justice has a very specific context.
Aristotle's father was a doctor in the court of the King of Macedon. Plato was from an aristocratic family. I seriously doubt that either Aristotle or Plato ever met any lepers, ever talked to poor people, ever hung out with fishermen.
The historical context of Jesus, Plato, Aristotle were totally different. And you cannot understand someone's moral, religious, or intellectual program apart from their life experience and historical context.
Plato and Aristotle were writing for other aristocrats and patricians with their programs of self-improvement, wisdom, self-cultivation, self-realization. Nonetheless, they have been wildly influential in the centuries that followed.
Jesus was a rabbi in Galilee, a backwater province that has been ravaged by war, starvation, oppression, and the theft of land from the small family farmers by the program of the Herodian Kings to turn Galilee into an agricultural feudal estate run by large landlords and farmed by indenture servants. Into this economic and historical context, Jesus was inspired to teach his message of social justice and the kingdom of God within us, which was largely intended for the poor, the sick, the oppressed.