Conceptually, I think the difference is between "ritual" or pastoral law and natural law.
Natural law is the law that is written on the human heart (see Deuteronomy), that is permanent, and that is knowable by all people. I'm no expert on the Levitical law, but I think these laws can be viewed as God's "pastoral laws."
For example, many of the societies surrounding Israel in Levitical times were polytheists and worshipped created things, like animals. Even Israel succumbed to worship of the golden calf.
So we see that God ordered the Jews to sacrifice animals on a continual basis. Perhaps one reason for this was pastoral, to prevent the Jews from worshipping animals.
Pastoral edicts are subject to changing cultural conditions. Natural law, on the other hand, is permanent: things like adultery, lying, idolatry, theft, murder, and coveting are always wrong.
This is reaffirmed in Scripture. In the New Testament, Paul continually reminds us that we are free from the Old Law. However, the "new" commandment, that we love God wholeheartedly and that we love our neighbor as ourselves, is far more sweeping than the Levitical laws or even the Ten Commandments because, not only are we prohibited from certain sins, but we are obligated to do good works.