"The true, to put it very briefly, is only the expedient in the way of our thinking, just as the right is only the expedient in the way of our behaving." (William James)
"Justice is the first virtue of social institutions, as truth is the first virtue of systems of thought." (John Rawls)
I would like to say that truth is a rightness in the way of belief, and justice is a rightness in the way of desire. Justice is the virtue of institutions, I agree; but truth is the correlative virtue of intuitions. If truth is the expedient in the way of thought, and I will grant that it may well be, then justice (arguably "the right") is the expedient in the way of feeling. The former is supported by the precision of our concepts, the latter by the precision of our emotions.
As to the way we behave, yes, we may in that regard be right or wrong, and, when this rightness or wrongness is conditioned by institutional factors, I will grant that that right is just and wrong is not. Truth, likewise, is the rightness of our beholding when such beholding is conditioned by intuition.
[Update: all behaviour is conditioned by institutions. And there can be no beholding without intuition. But they can be, as it were, "barely" conditioned. We might perhaps talk of "unbound" behaviour and beholding: actions that lack any immediate motive, beholdings that don't immediately make sense.]