Which came first Original Guilt or Original Sin?

The federal headship of Adam may not seem germane to a descriptive psychology of human nature. As an office or function it does not even describe Adam's nature. But without it there is no understanding of the later generations - Cain, Lamech, Paul, and Alexander the coppersmith. Much of this material has already been touched upon, so that a reminder, some implications, and a small addition will be sufficient here. The small addition will be a defense of the consistency of immediate imputation with the philosophy of Realism, a consistency which Hodge denies.
In the discussion on traducianism it was necessary to anticipate the doctrine of immediate imputation. The essential point was there made clear: Depravity is a part of the penalty for sin, therefore the guilt logically precedes. The question is, on what ground does God hold us, Adam's posterity, guilty? The Biblical doctrine is that God imputes Adam's guilt to us immediately; that is, without an intermediary step. The word immediately here does not refer to time. One might say that God imputed Adam's guilt to us the very moment that Adam sinned. This could well be true, though it is more accurate to say that God imputed this guilt from all eternity. Clearly the doctrine of immediate imputation does not focus on time, as the contemporary usage of the word might suggest: The question is as stated above: Does God impute guilt because of our inherited depravity, or does he impute it without this as a means? The Biblical reason for the doctrine of immediate imputation is that depravity is a part of the penalty the guilt entails. We are not guilty because we are depraved; we are depraved because we are guilty.
Of course we are also guilty of our own voluntary transgressions here and now. This, however, is irrelevant to the present matter. The present matter is our relation to Adam's first sin.
The Westminster Confession uses a very carefully phrased paragraph to distinguish between inherited depravity and imputed guilt. It is so carefully yet so naturally worded that most readers probably fail to see the implications. The confessional statement is: 'They being the root of all mankind, the guilt of this sin was imputed, and the same death in sin and corrupted nature conveyed to al their posterity descending from them by ordinary generation' (VI, 3). Note: the guilt was imputed; the corruption was conveyed. - Gordon H. Clark, The Biblical Doctrine of Man