The primary difference is that of motivation. In religion, we try to obey the divine standards out of fear. We believe that if we don't obey we are going to lose God's blessing in this world and the next. In the gospel, the motivation is one of gratitude for the blessing we have already received because of Christ. While the moralist is forced into obedience, motivated by fear of rejection, a Christian rushes into obedience, motivated by a desire to please and resemble the one who gave his life for us.
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The Christian gospel is that I am so flawed that Jesus had to die for me, yet I am so loved and valued and that Jesus was glad to die for me.
The Reason for God: Belief in an Age of Skepticism by Timothy Keller, pp 186-187