Plato's definition of Justice is found in The Republic at Bk IV, Section 433 b, where Socrates says: "Justice is to DO one's own business." [Paul Shorey translation; Benjamin Jowett translation KB] Other translations/commentators read that "Justice is to MIND one's own business."
But that leaves a huge open question which is:- "What is my own business?", to answer. For Plato, his guardians and "philosopher - King" in his ideal Republic/polity would know what everyone's business in the 3 classes was and, in essence, tell us plebeians (since average people or "plebs" is what the majority of citizens will always be) what to do.
Aristotle went a bit further than a mere "Platitude" (which was true but still left that huge "open question" --- What is my own business?) in defining Justice as: "...the lawful and the fair." On the contrary injustice was defined by Aristotle as, "... the unlawful and the unfair.", in the Nicomachean Ethics at Bk V., Ch. 1., 1129a line 35 (approximate).
But, once again, Aristotle has to explain both just vs. unjust laws and fair vs unfair practices/actions of human beings --- which he does, subsequent to his original definitions of justice and injustice, in subsequent statements of Ch. 1 of Bk V. and in subsequent chapters of Bk V. What he says in the subsequent chapters is far more intelligible in light of his general definition of VIRTUE as middle point (a "mean") between contrary vices --- something which Plato never did in his various dialogues concerning either justice (e.g. The Republic) or other virtues (e.g. Meno)
In those subsequent chapters of Bk. V of The Nicomachean Ethics you may read that Justice is a "proportion" obtained by treating equals, equally and unequals, unequally, so as to effect (bring about) the common good. (which is a better definition of justice). But in the first chapter of Bk V, you can read Aristotle say, quote:
ARISTOTLE:
"Now 'justice' and 'injustice' seem to be ambiguous [have 2, or more than 2, meanings; KB], but because their different meanings approach near to one another the ambiguity escapes notice and is not obvious as it is, comparatively, when the meanings are far apart, e.g. ... "
So there are several meanings and definitions of justice, according to Aristotle. But what Aristotle and Plato both have in common is the POLITICAL nature of justice [Plato: Doing one's own business in an ideal political state; and Aristotle: "the just is the LAWFUL and fair" because law-making is the business of politicians and political entities] Thus Aristotle also says in Ch. 1. of Bk V, quote:
ARISTOTLE:
"... so that in one sense we call those acts JUST that tend to produce and preserve happiness and its components for the POLITICAL society... (snip)... This form of justice is complete virtue, but not absolutely, but in relation to our neighbor." [1129b line 17 ...(snip)... line 26]
Thus it is not really a case of "Plato vs. Aristotle", but, rather, a case of Aristotle embellishing and clarifying Plato's broad definition of justice from The Republic [Justice is to do one's own business.] and also giving a definition of virtue (which Plato did not provide in his dialogues) which helps "sort out" ambiguous definitions of justice.
Kevin