Christ himself used the image of Matrimony as a model for understanding his relationship with the Church and with each one of us. So I think it is helpful to think about questions like this in the context of a marriage.
If a man were to come home after a hard day’s work and snap unjustly at his wife, he would commit an offense against her. This offense would harm their relationship to some greater or lesser degree. But being a loving and understanding wife, she simply overlooks his offense and forgives him before he even has time to apologize, because she knows that he really does love her. At the very least, she is ready to forgive him at the slightest hint of sorrow on his part, even if it’s not explicit. Knowing he is upset at the day’s events, she may even do something special for him to make him feel better. The harm he did to their relationship is more than made up for by her forgiveness and generosity.
On the other hand, if she were to catch him committing adultery against her, then their relationship would not just be “damaged,” but rather it would be fundamentally broken. She may be ready and willing, even anxious, to forgive him, but any expression of “love” to her would be a lie until he acknowledged his offense and explicitly sought her forgiveness. If she were to simply ignore the adultery, she would be denying her own dignity and would be aiding and abetting future occurrences of this sin by her husband. Any genuine repair of their relationship absolutely requires an explicit acknowledgment of the offense by the husband, a sincere request for her forgiveness, and a firm intent never to commit adultery again.
It is the same in our relationship with God. The first case above is an example of a venial sin. God forgives venial sins very readily, often because He knows we really love Him, despite our minor transgression. Our minor offense damages our relationship with him, but does not fundamentally rupture it.
The second case above is an example of a mortal sin. It fundamentally ruptures our relationship of love, and it cannot be fixed without an explicit acknowledgment of guilt, sincere request for forgiveness, and a firm purpose of amendment. Certainly God is always ready to forgive even the most heinous sin. But such forgiveness requires an explicit act of sorrow on our part and the firm resolution to always avoid this sin in the future.