I can compare the two in this way:

Sin, according to the Scriptures, is said to be in the flesh; whereas sins are in our conduct.

Sin is a principle in us; it is a principle of the life we have. Sins are acts committed by us; they are acts in our living.

Sin is a law in the members. Sins are transgressions that we commit; they are activities and real acts.

Sin is related to our being; sins are related to our doing.

Sin is what we are; sins are what we do.

Sin is in the realm of our life; sins are in the realm of the conscience.

Sin is related to the power of the life we possess; sins are related to the power of the conscience. A person is governed by the sin in his natural life, but he is condemned in his conscience by the sins committed outwardly.

Sin is something considered as a whole; sins are something considered case by case.

Sin is inside man; sins are before God.

Sin requires our being made free; sins require our being forgiven.

Sin is related to sanctification; sins are related to justification.

Sin is a matter of overcoming; sins are a matter of having peace in one's heart.

Sin is in man's nature; sins are in man's ways.

Figuratively speaking, sin is like a tree, and sins are like the fruit of the tree.

We can make this matter clear with a simple illustration. In preaching the gospel, we often compare the sinner to a debtor. We all realize that to be a debtor is not a pleasant matter. But we must remember that it is one thing for a man to have debts; it is another thing for a man to have a disposition for incurring debts. A person who borrows again and again is not that concerned about using others' money. The Bible says that Christians should not be debtors (Rom. 13:8); they should not borrow from others. A person with a borrowing disposition may borrow two or three hundred dollars from someone today, then two or three thousand dollars from someone else tomorrow. Even if he is unable to pay back his debts, and his relatives or friends have to pay back the money for him, after a few days he will begin to consider borrowing again. This shows that to borrow is one thing, but to have a borrowing disposition is another. The sins that the Bible describes are like the outward debts, while sin is like the inward habit and disposition; it is like the mind that is inclined to borrow easily. A person with such a mind will not stop borrowing just because someone else has paid his debts. On the contrary, he may borrow even more because others are now paying his debts.

This is why God is dealing not just with the record of sins, but also with the inclination toward sin. We can see that it is important to deal with the sins, but it is equally important to deal with sin. Only when we see both of these aspects can our understanding of our salvation be complete.