One of the differences between sin and transgression is “Knowledge” the other is “Will” or “intent”. If we act having a certain knowledge and have the intent to do evil, then we sin. If we lack either “will/intent” or “knowledge”, then we transgress. The beautiful thing about this is that Transgressions are covered by the atonement WITHOUT conditions. Sins on the other hand require repentance to receive forgiveness. When I say that transgression requires knowledge, I do not mean the belief in something simply because the prophet said it. I mean knowing it first hand. Even though the prophet Alma told the taught the people, he said that this only caused them to have reason to believe but that even though he was the prophet and was teaching them, this did not give them the knowledge enough to sin.
Sin is to act KNOWINGLY AND WILLINGLY against the will of God. = Requires repentance to receive forgiveness.
Transgression is to act UNKNOWINGLY AND/OR UNWILLINGLY against the will of God. = Covered by the atonement without repentance.