The difference between the two is this:
Injustice is any action that enforces an unfair consequent upon one in excess of the offense committed or a completely undeserved consequent for the benefit of one over another.
Unjustice is different in that it would be defined as warping true justice to serve ones own ends. Anyone who would do this is deem ‘unjust’ and has not justice in their hearts and so, cannot truly expect anything more than true justice in return. Justice for the unjust would be a fair consequent depending upon the injustice(s) or unjustice(s) they have committed.
If one should let emotion rule over justice, that one would also be guilty of unjustice and would hence be a hypocrite.