Isaiah 53:5
But he was pierced for our transgressions, he was crushed for our iniquities; the punishment that brought
There’s a decent explanation of the penal substitution versus the satisfaction theory of our atonement on wikipedia. Here’s a snippet:
“The classic Anselmian formulation of the satisfaction view should be distinguished from
penal substitution. Both are forms of satisfaction doctrine in that they speak of how Christ’s death was
satisfactory, but penal substitution and Anselmian satisfaction both offer different understandings of how Christ’s death was satisfactory. Anselm speaks of human sin as defrauding God of the honour he is due. Christ’s death, the ultimate act of obedience, brings God great honour. As it was beyond the call of duty for Christ, it is more honour than he was obliged to give. Christ’s surplus can therefore repay our deficit. Hence Christ’s death is
substitutionary; he pays the honour
instead of us. Penal substitution differs in that it sees Christ’s death not as repaying God for lost
honour but rather paying the
penalty of death that had always been the moral consequence for sin (e.g. Genesis 2:17; Romans 6:23). The key difference here is that for Anselm, satisfaction is an
alternative to punishment, “The honor taken away must be repaid, or punishment must follow” (Cur Deus Homo Bk 1 Ch 8). By Christ satisfying our debt of honor to God, we avoid punishment. In Calvinist Penal Substitution, it is the punishment which satisfies the demands of justice.
Another distinction must be made between penal substitution (Christ
punished instead of us) and substitutionary atonement (Christ suffers
for us). Both affirm the substitutionary and vicarious nature of the atonement, but penal substitution offers a specific explanation as to what the suffering is for:
punishment. Nearly all of the Church Fathers, including Justin Martyr, Athanasius and Augustine teach substitutionary atonement. Indeed, the doctrine was clearly articulated by the prophet Isaiah in 800 BC. However the specific interpretation as to what this suffering for sinners meant differed. The early Church Fathers, including Athanasius and Augustine taught that through Christ’s suffering in humanity’s place, he overcame and liberated us from death and the devil. Thus while the idea of substitutionary atonement is present in nearly all atonement theories, the specific idea of satisfaction and later penal substitution are later developments in the Latin church.”
Hope that helps.
David