What is the difference between original sin and imputed sin?
The terms "original sin" and "imputed sin" refer to the two main effects that Adam's sin had on the human race.
First, as a result of Adam's sin we all enter the world with a fallen nature. This is original sin--the sinful tendencies, desires, and dispositions in our hearts with which we are all born. Thus, original sin is something inherent in us--it is a morally ruined character. The original sin that we are all born with manifests itself throughout our lives in actual sins--the actions, thoughts, and feelings we have that violate God's moral commands. So our sinful hearts (original sin) cause us to make sinful choices, think sinful thoughts, and feel sinful feelings (actual sins). We are not sinners because we sin; rather, we sin because we are sinners. We are all born totally imprisoned in original sin. There is no island of goodness left in us.
Second, the guilt of Adam's sin is credited not just to Adam himself, but to us all. We are regarded as having sinned in Adam, and hence as deserving of the same punishment. This is imputed sin. Thus, we not only receive polluted and sinful natures because of Adam's sin (original sin), but we are also regarded as having sinned in Adam such that we are guilty of his act as well (imputed sin). Imputed sin is the ruin of our standing before God and is thus not an internal quality but an objective reckoning of guilt, whereas original sin is the ruin of our character and thus is a reference to internal qualities. Both original sin and imputed sin place us under the judgment of God.
Since the consequences of Adam's sin are twofold (original sin and imputed sin), the remedy of our salvation is also twofold. John Piper writes:
So we have seen two things that need a remedy. One is our sinful nature that enslaves us to sin, and the other is our original guilt and condemnation that is rooted not first in our individual sinning but in our connection with Adam in his sin. The book of Romans—indeed the whole Bible— is the story of how God has worked in history to remedy these two problems. The problem of our condemnation in Adam God remedies through justification in Christ. The problem of our corruption and depravity he remedies through sanctification by the Spirit. Or to put it another way: The problem of our legal guilt and condemnation before God is solved by his reckoning to us the righteousness Christ; and the problem of our moral defilement and habitual sinning is solved by his purifying us by the work of Spirit. The first remedy, justification, comes by imputed righteousness. The other, sanctification, comes by imparted righteousness. Justification is instantaneous; sanctification is progressive – and we will deal extensively with it in Romans 6-8, just we have dealt with justification in Romans 3-5. (John Piper, "Adam, Christ, and Justification: Part IV")
John Murray, The Imputation of Adam's Sin.
Wayne Grudem, Systematic Theology, chapter 24, "Sin"
Jonathan Edwards, The Great Christian Doctrine of Original Sin Defended in The Works of Jonathan Edwards Volume I, pp. 143-233.