According to Catholicism, what is the difference between forgiveness and release from punishment?

Question

The first thing to note is that forgiveness of a sin is separate from punishment for the sin. Through sacramental confession we obtain forgiveness, but we aren't let off the hook as far as punishment goes.

That's a quote from Catholic Online's article on indulgences. I've never heard forgiveness spoken about in this way. Even the site's tag wiki for forgiveness specifically includes release from punishment. I know this question is similar, but its answers don't cover a Catholic view. The only well-sourced answer explains a Lutheran stance.

If God's forgiveness does not spare one from punishment, then what is it? Does this mean that the sacrament of confession alone does not spare you from punishment? Where does the Catholic Church get this distinction? Is there a biblical basis? Is it part of sacred tradition? Did a council decide it?

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On another note, I learned while researching for this question that anyone who has completed the three prerequisites for an indulgence may gain one by participating on Christianity.SE:

20. Christian Doctrine. Partial indulgence to those who take part in teaching or learning Christian doctrine.

Answer 1

According to Catholic theologians I have listened to, there is a difference between sins that are forgiven and the release of punishment due to sin.

1) Admitting a sin and asking for and receiving forgiveness.

2) Then, reparation for the damage caused by the sin. The term "punishment" for sin is not usually used because it makes God sound kind of vengeful.

The example usually given by these theologians on EWTN radio, etc. is: Johnny breaks a window and is sorry for his mistake and asks for forgiveness from his father who then forgives him. However, he still needs to fix the broken window which is the reparation.

I personally find this type of official explanation of part 2) rather weak because many, many sins cannot be repaired in a normal sense. For one thing, the person that was hurt may have died. Or, Johnny may not have any glass and glazing skills and dad will have to fix the window. Actually, this is the rationale of the Catholic church for purgatory. Purgatory allows a period (non-time specific) of reparation for your sins if they were not adequately repaired while alive. I am of the Catholic Church, but I question several dogmas/doctrines/beliefs.

I hope this information contributes—this is my first answer given.