It is tempting to file the Buddhist analysis of harmful action as another tradition's doctrine of sin, in a milder key. It is not that, and the mismatch is structural rather than a matter of severity.
Sin, in the traditions that use the word, requires a lawgiver. There is a command, an authority behind it, a breach, and a question of pardon. Every one of those terms is missing here. What the Buddhist texts assess is whether an act is kusala or akusala, wholesome or unwholesome, sometimes rendered skilful and unskilful, and the assessment is made on two grounds: the state of mind the act grows out of, and what the act produces. An unwholesome act is not unwholesome because a rule forbade it. It is unwholesome because it grows from greed, hatred or delusion, and because it ripens into suffering.
Two consequences follow that a reader coming from a juridical model will not expect. The first is that the precepts are not commandments. The five a lay follower takes are phrased as training rules that the speaker undertakes, in the first person, and breaking one incurs no penalty from any authority, because no authority imposed it. The second is that there is nothing here to forgive, since nobody occupies the position from which forgiveness would be given. What has been done ripens; the useful question is what to do now.
Monastic practice has to be described carefully, because it looks like an exception. The Vinaya does have confession of offences, and the fortnightly recitation of the code is preceded by monks declaring theirs. That procedure restores a monk's standing in his community, which is a real and important thing. It is discipline, and it does not undo a karmic result.