Justice, equity are comparable primarily in their legal uses and when they denote the act, practice, or obligation of giving or rendering to a person or thing what is his or its due (as in conformity with right, truth, or the dictates of reason).
Justice is by far the wider-ranging term, for it may apply to an abstraction which represents an ideal or to a quality of mind which exhibits adherence to this ideal or to a quality in a thing which never departs from the truth in the slightest degree or to the treatment accorded one who has transgressed a law, whether a divine law, a natural law, or the law of a state, or who seeks relief when wronged or protection when his rights are threatened or to the system of courts of law whereby the rights of an individual or his innocence or guilt are determined in accordance with the laws of the state.
Equity differs from justice chiefly in being more restricted in its denotation, for it usually implies a justice that transcends the strict letter of the law and is in keeping with what is reasonable rather than with what is merely legal. It is in this sense that a court of equity is, theoretically at least, distinguished from a court of law.
To the former go for adjudication and settlement the unusual cases where abstract justice might not be dealt out according to the limitations of the written law while to the latter go the vast majority of cases where the determination of facts is of first importance and where the law, once the facts are established, provides the treatment to be accorded the person or parties involved. But equity in nonlegal use implies a justice based upon a strictly impartial meting out of what is due (as rewards and punishments or praise and blame).