Moral sacrifice means someone dies as a result of his/her opposition to power and his/her advocating for the poor and the oppressed. Jesus's death is close to this type. Sin-offering or sin sacrifice means that something is offered to God, usually animal sacrifice, to atone for sins. In the Old Testament, there has never been human sin-offering. Humans are atoned for their sins through the rituals of Yom Kippur and through their repentance. Except for Hebrews or some later epistles in the New Testament, there is no sense that Jesus's death is considered a sin offering. In the Gospels and Paul's authentic letters, Jesus's death is close to moral sacrifice. For example, in the Gospel of Mark, Jesus's death is not needed for the forgiveness of sin since people can repent at baptism. His death is the result of his proclaiming God's good news and his kingdom, not Rome's good news or Caesar's kingdom. The exception to this is seen in Heb 10:9-12 where Jesus's death is a sin offering:
9 He abolishes the first in order to establish the second. 10 And it is by God’s will that we have been sanctified through the offering of the body of Jesus Christ once for all. 11 And every priest stands day after day at his service, offering again and again the same sacrifices that can never take away sins. 12 But when Christ had offered for all time a single sacrifice for sins, “he sat down at the right hand of God.”