Hodge:

2. The Difference between a penal and a pecuniary satisfaction.–These differ precisely as do crime and debt, things and persons, and therefore the distinction is both obvious and important. Many, who either are incapable of understanding the question, are ignorant of its history, or who are unscrupulous as to the manner in which they conduct controversy, are continually charging our doctrine with the folly of representing the sacrifice of Christ as a purely commercial transaction, in which so much was given for so much, and in which God was in such a sense recompensed for his favours to us that however much gratitude we may owe to Christ, we owe on this behalf none to God. Long ago the doctrine of the Reformed Churches was unanswerably vindicated from such puerile charges by all its most authoritative expounders. “Here the twofold solution, concerning which jurists treat, should be accurately distinguished. The one, which ipso facto liberates the debtor or criminal because that very thing which was owed is paid, whether it was done by the debtor or by another in his name. The other, which ipso facto does not liberate, since not at all the very thing which was owed, but an equivalent, is paid, which, although it does not thoroughly and ipso facto discharge the obligation, yet having been accepted–since it might be refused–is regarded as a satisfaction. This distinction holds between a pecuniary and a penal indebtedness. For in a pecuniary debt the payment of the thing owed ipso facto liberates the debtor from all obligations whatsoever, because here the point is not who pays, but what is paid. Hence the creditor, the payment being accepted, is never said to extend toward the debtor any indulgence or remission, because he has received all that was owed him. But the case is different with respect to a penal debt, because in this case the obligation respects the person as well as the thing; the demand is upon the person who pays as well as the thing paid; i.e., that the penalty should be suffered by the person sinning; for as the law demands personal and proper obedience, so it exacts personal enduring of the penalty. Therefore, in order that a criminal should be absolved–a vicarious satisfaction being rendered by another hand–it is necessary that there should intervene a sovereign act of the supreme law-giver, which, with respect to the law, is called relaxation, and with respect to the debtor is called remission, because the personal endurance of the penalty is remitted, and a vicarious endurance of it is accepted in its stead. Hence it clearly appears that in this work (of Redemption) remission and satisfaction are perfectly consistent with each other, because there is satisfaction in the endurance of the punishment which Christ bore, and there is remission in the acceptance of a vicarious victim. The satisfaction respects Christ, from whom God demanded the very same punishment, as to kind of punishment, though not as to the degree nor as to the nature of the sufferings which the law denounced upon us. The remission respects believers, to whom God remits the personal, while he admits the vicarious punishment. And thus appears the admirable reconciliation of justice and mercy–justice which executes itself upon the sin, and mercy which is exercised towards the sinner. Satisfaction is rendered to the justice of God by the Sponsor, and remission is granted to us by God. (Turretin, Locus XIV. Quaestio 10.)

Hence pecuniary satisfaction differs from penal thus: (a.) In debt, the demand terminates upon the thing due. In crime, the legal demand for punishment is upon the person of the criminal. (b.) In debt, the demand is for the precise thing due–the exact quid pro quo, and nothing else. In crime, the demand is for that kind, degree and duration of suffering which the law–i.e., absolute and omniscient justice–demands in each specific case, the person suffering and the sin to be expiated both being considered. (c.) In debt, the payment of the thing due, by whomsoever it may be made, ipso facto liberates the debtor, and instantly extinguishes all the claims of the creditor, and his release of the debtor is no matter of grace. In crime, a vicarious suffering of the penalty is admissible only at the absolute discretion of the sovereign; remission is a matter of grace; the rights acquired by the vicarious endurance of penalty all accrue to the sponsor; and the claims of law upon the sinner are not ipso facto dissolved by such a satisfaction, but remission accrues to the designed beneficiaries only at such times and on such conditions as have been determined by the will of the sovereign, or agreed upon between the sovereign and the sponsor.

Archibald Alexander Hodge, The Atonement (London: T. Nelson And Sons, 1868), 33-35.

Credit to Tony

Packer:

The Truth about the Reformers to be this They habitually spoke of atonement in the language of legal representation. Christ, they said, personam nostram sustinuit at the bar of God, enduring the penalty of the broken law in man’s place. But they did not distinguish the two possible ways in which the notion could be developed, nor opt for one rather than the other. The transaction as they described it could be thought of after the analogy either of civil or of criminal law. In the first case, Christ would have paid our debt, the second our penalty. In the first case, his righteousness would be imputed to the believer in its effects: to say that Christ’s righteousness is reckoned his would then be merely a way of saying that he receives the benefit of legal immunity and as a result of Christ’s intervention on his behalf. Christ paid the debt; therefore he himself need never pay it. Such a conception, is simple. But if the transaction were interpreted in the second way, as a case of penal substitution, the idea becomes more difficult and the pitfalls more numerous. This way in fact the main strand in the Reformers’ thought. On the first view, the ground of the sinner’s acquittal from liability to punishment (i.e., his justification) is the fact that Christ paid the debt he had incurred. On the second view, the ground of justification is God’s attribution (imputation) of Christ’s obedience and suffering to the guilty sinner. The notion is Biblical, but demands careful statement, which in the early days of Protestant theology it did not always receive. In those days, the two lines of thought existed side by side in the minds of the some men without any awareness of inconsistency. Both served to illustrate the position which it was the Reformers’ supreme concern to demonstrate and defend, that the sinner’s justification is secured, not by his own work, but by his faith in the work Christ did on his behalf. To illustrate this point yet further, they sometimes permitted themselves to speak as if Christ became a sinner in fact at Calvary, and as a man becomes righteous in fact when he believes. During the century which followed, Protestant theologians devoted themselves to the task of systematizing, polishing and defending the Reformers’ teaching. One of the results of these analytical labours was the discovery of inconsistency between these two lines of thought concerning Christ’s satisfaction for sin . Hence arose controversy concerning the nature of imputed righteousness.

James I. Packer, “The Redemption and Restoration of Man in the Thought of Richard Baxter: A Study in Puritan Thought,” (Ph.D diss.,University of Oxford, 1954), 276-277. [Note, what he says, in my opinion, was also as true for many of the later Puritans.]