As he explained it, and I understand it, this is about the difference between something just being a sin and it being a 'crime' as far as the Catholic Church is concerned. Sins are forgiven by God and in the Sacrament of Penance, the Priest merely acts as an intermediary for the forgiveness of sin - but the sacrament also involves reconciliation with the Church, and that part of it is done by the Priest.
These very serious offences involve a violation of Church law to such an extent that a normal Priest is not considered qualified to decide whether the person has reconciled with the Church. The sin is forgiven - that's between the person and God - but whether the person is reconciled with the Church requires an expert to question and satisfy themselves that the person understands the Church law in question.
If a person confesses one of these special class of sins to a 'normal' priest, the sin is forgiven as any sin is forgiven by God - but the Priest should refer the person to a higher authority to resolve the question of whether they are following Church law.
The breach of Church law is less important than the sin, but may be more complex to resolve. God forgives simply because a person sincerely repents and there is nothing complex about that. But the Church is not as perfect as God.
I hope I've done justice to what I was told. It seemed to make sense to me at lunch.
If this is true, then why does the priest hearing the confession, then assign tasks that must be done (such as: say 20 Hail Marys and $20 in the collection box) in addition to Christ's forgiveness through Grace? If Christ's death on the cross is sufficient, why are the additional tasks necessary or warranted?
It seems to me that your Jesuit Priest is inferring that the church, because it is not perfect, can demand punishment (or whatever it wants to call it). If the church is demanding this "punishment" in order that the sinner be allowed to remain a member of the church, then either the church does not truly believe that Christ's death on the cross is sufficient for Grace, or (could it be) that the church sees an opportunity to (and I will put it quit bluntly) "blackmail" the sinner by saying that we cannot allow you to remain a member unless you do this and this and this for us.
Welcome home, I will pray for you during Lent. I am sure you have realized that FR has many people who are misinformed about the Church. Somehow they remain that way as they ask questions but do not seek answers.