I’ve been looking for some “documentation” on the distinction between absolution and forgiveness. Try this quote from the Summa
newadvent.org/summa/4084.htm#article3
Objection 3. Further, to absolve from sin is the same as to remit sin. But God alone remits sin, for He alone cleanses man inwardly from sin, as Augustine says (Contra Donatist. v, 21). Therefore it seems that God alone absolves from sin. Therefore the priest should say not: “I absolve thee,” as neither does he say: “I remit thy sins.”
Reply to Objection 3. God alone absolves from sin and forgives sins authoritatively; yet priests do both ministerially, because the words of the priest in this sacrament work as instruments of the Divine power, as in the other sacraments: because it is the Divine power that works inwardly in all the sacramental signs, be they things or words, as shown above (62, 4; 64, 1,2). Wherefore our Lord expressed both: for He said to Peter (Matthew 16:19): “Whatsoever thou shalt loose on earth,” etc., and to His disciples (John 20:23): “Whose sins you shall forgive, they are forgiven them.” Yet the priest says: “I absolve thee,” rather than: “I forgive thee thy sins,” because it is more in keeping with the words of our Lord, by expressing the power of the keys whereby priests absolve. Nevertheless, since the priest absolves ministerially, something is suitably added in reference to the supreme authority of God, by the priest saying: “I absolve thee in the name of the Father, and of the Son, and of the Holy Ghost,” or by the power of Christ’s Passion, or by the authority of God. However, as this is not defined by the words of Christ, as it is for Baptism, this addition is left to the discretion of the priest.
If forgiveness and absolution were two different words for one reality, St. Thomas would not have used the words “and” & “both.” He’s actually making a distinction between forgiveness and absolution (in his response to the objection), especially by saying that the absolution is expressed in Matthew, and forgiveness in John.
We need to keep in mind that when one is absolved, one is likewise forgiven. Absolution and forgiveness together form the total reconcilliation which occurs in the Sacrament.
Is this making more sense now?