You didn't ask about Reformed, but I'll answer anyway.
The answer is "both".
I wouldn't use the word covered, so much as forgiven. Calvin said that through a mystical union with Christ, we have a "fellowship of righteousness." This plays much the same role as theosis for Orthodox. The fellowship of righteousness has also been referred to as exchange. Through it, Christ takes on our sins. He suffers for them on the cross, and is victorious over them in the resurrection. With his resurrection he wipes out their ability to separate us from God. Also through this fellowship, we experience his obedience and his victory.
So there are two implications of the union with Christ. First, God forgives our sins. I wouldn't say it's as if they had never existed, since God still has to help us overcome them. But they no longer form a barrier between us and God, partly because they are forgiven, and partly because Christ has joined us on our side of the barrier, by uniting himself with sinners.
Second, the union with Christ forms the basis through which God regenerates us.
In Reformed thought, God doesn't stop with forgiveness, nor should we want him to. His commitment to us includes making us whole again, and this is something any Christian would want. During this life we are simultaneously justified and a sinner. But we're on a path to healing.
Luther had a delight in extreme images. He originated the image of the snow-covered dungheap. That could leave the impression that God leaves us in our sin, and just sticks a white tarp over us. But that's not the only thing he about this topic. He noted that we are like a patient who has put himself in the hands of a competent doctor. While he's still sick, he's started to envision himself as getting well, and in some contexts can be regarded as well. We're justified, i.e. in good standing before God, because we've put ourselves in his hands. He sees his own image, in the form of Christ, in us, even if not perfectly, at least he knows that's where we're going. Even when we fall back. (Unlike Catholics, we don't think serious sin normally removes our status as one of God's people.) As long as we remain his, it's more like a setback during treatment of an illness. We may temporarily need discipline, but we're still his children.
God says He will remove our sins from us as far as east is from the west.
). Remission is ripping out the entire page and discarding it.
