Will Allah forgive or ease the punishment?

I recently converted to Islam, and there are things that I don't understand. However, I am seeking answers. I have read a lot about how Allah forgives a person's sins if they sincerely repent from the heart, feel genuine regret, and strive not to repeat them. However, I came across an article on the internet that is unclear to me. Here is a quote from the article: "The first way to avoid or mitigate the punishment of Allah is sincere repentance. If a Muslim sincerely repents of a sin after committing it, then this repentance can contribute to the weakening of the punishment or forgiveness." This statement mentions both weakening the punishment and forgiveness. Does this mean there are cases where Allah may not completely forgive a sin but instead lessen the punishment? What exactly is being conveyed here? Is this an established Islamic teaching, or is it just the author's interpretation and should not be taken literally?