- Guilt is knowing you have done something wrong.
- Shame is feeling that you are something wrong.
A detailed and insightful article on this is available here.
Shame can haunt you long after you’ve experienced forgiveness for a past mistake. And unlike guilt, shame has a contagious quality so it spreads to the people around you. The alcoholic embarrasses his whole family. The promiscuous daughter brings shame on her parents. The children of divorced parents feel marked by that separation for decades. And divorced people themselves struggle with a seemingly inescapable black mark of shame. 
As in the previous article, here we see how the Gospel addresses our needs at both levels. God’s mercy forgives our sin as Jesus was pronounced guilty in our place. And God’s grace goes further to declare us righteous in Christ, placing all of our shame upon Him as well and giving us His full acceptance and approval instead. Other people may still look down on you for your failings, but once you belong to Jesus God no longer does. He looks on you with the perfect delight of a Father who could not be more pleased with you.
When you stand before God (if you belong to Jesus by faith) then He will say to you, “Well done my good and faithful servant,” not because YOU have lived an impressive life but because you have been given credit for the infinitely impressive life of Jesus.
You can trade your guilt for Jesus’ righteousness and your shame for His glory! That is how good the Good News really is!