Hodge:

1) The word satisfaction is the one which for ages has been generally used to designate the special work of Christ in the salvation of men. With the Latin theologians the word is “satisfactio,” with the German writers, “Genugthun,” its exact etymological equivalent, “the doing enough.” By the satisfaction of Christ is meant all He has done to satisfy the demands of the law and justice of God, in the place and in behalf of sinners. This word has the advantage of being precise, comprehensive, and generally accepted, and should therefore be adhered to. There are, however, two kinds of satisfaction, which as they differ essentially in their nature and effects, should not be confounded. The one is pecuniary or commercial; the other penal or forensic. When a debtor pays the demand of his creditor in full, he satisfies his claims, and is entirely free from any further demands. In this case the thing paid is the precise sum due, neither more nor less. It is a simple matter of commutative justice; a quid pro quo; so much for so much. There can be no condescension, mercy, or grace on the part of a creditor receiving the payment of a debt. It matters not to him by whom the debt is paid, whether by the debtor himself, or by someone in his stead; because the claim of the creditor is simply upon the amount due and not upon the person of the debtor. In the case of crimes the matter is different. The demand is then upon the offender. He himself is amenable to justice. Substitution in human courts is out of the question. The essential point in matters of crime, is not the nature of the penalty, but who shall suffer. The soul that sins, it shall die. And the penalty need not be, and very rarely is, of the nature of the injury inflicted. All that is required is that it should be a just equivalent. For an assault, it may be a fine; for theft, imprisonment; for treason, banishment, or death. In case a substitute is provided to bear the penalty in the place of the criminal, it would be to the offender a matter of pure grace, enhanced in proportion to the dignity of the substitute, and the greatness of the evil from which the criminal is delivered. Another important difference between pecuniary and penal satisfaction, is that the one ipso facto liberates. The moment the debt is paid the debtor is free, and that completely. No delay can be admitted, and no conditions can be attached to his deliverance. But in the case of a criminal, as he has no claim to have a substitute take his place, if one be provided, the terms on which the benefits of his substitution shall accrue to the principal, are matters of agreement, or covenant between the substitute and the magistrate who represents justice. The deliverance of the offender may be immediate, unconditional, and complete; or, it may be deferred, suspended on certain conditions, and its benefits gradually bestowed.

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