True guilt is the fruit of a healthy conscience that reflects the law of God to us and lets us know that we owe a moral debt to God because of our disobedience (Romans 2:15). Now we can have a false feeling of guilt when we take the responsibility for another person’s actions which are always outside of our control or about something we have no control over. Guilt is good if we use it to make us aware of our need of the sacrifice of the Lord Jesus for our sins and that our only hope of forgiveness and salvation is in HIM. If we try to pay for our guilt by our own actions then this leads us down the road of legalism and many times self condemnation and depression.
Conviction of the Holy Spirit (John 16:8) is a work of the Holy Spirit that is an additional revelation of our need of Christ to save us. The Holy Spirit breaks through even a seared conscience and makes us aware of our moral failings. He also shows us the true path of righteousness we should have taken. In addition He points us to the day of judgement so that we can see that our only hope of forgiveness is the grace of God found in Christ Jesus’ sacrifice for our sins and resurrection from the dead.
So the difference between guilt and conviction is that guilt is the fruit of the law of God that has been written into the soul of every human being and conviction is the direct revelation into the soul of our moral failure by the Holy Spirit. Both are given to make us aware of our need of Christ to save us and aid in creating repentance in our hearts over our sins. Neither guilt or conviction need to lead to feelings of being justly condemned by God for our wrong doing but instead call us to know the forgiveness and justification we can find only in Christ Jesus. However, if we don’t turn to the sacrifice of Christ then they both would warn us that we will face condemnation on judgment day justly for our sins. God’s purpose in both is to motivate us to seek Jesus as our Savior and Lord.