What are the differences between case law and written law?

All laws are written. I suspect that you are thinking of Statute Law.

Statute law is the body of laws produced by the legislature (parliament in the UK). Statutes are drafted as best they can be to suite as many combinations of circumstances that the legislators can think of. That's what new laws take so long to produce.

Case Law is the body of law produced in the courts as a result of judges "interpreting" staute laws to more tightly reflect the circumstances of individal cases. Courts also build up a body of decisions based on precedent, which is what earlier courts decided on similar cases. This body of law goes back over 1000 years and is generally known as Common Law.

Because of the way that it is developed the Common Law is able to react and change readily to the social and moral trends of the nation. For example - the common law sensitivity to social attitues meant that few people were hanged for murder long before the death penatly was abolished by statute.

The statute laws take longer to produce but they are better able to respond to technological and political changes. One of the best examples of this in recent years is the Data Protection Act which covers privacy of personal records held by computers. This was something that the common law could not do, because computers are realtively new. But eventually data protection will become part of common law.

Written law is the formal stuff assembled by legislatures. It's the stuff on the books that formally defines crimes, etc.

Case law is that established via the courts, as they set precedent in how they interpret the formal written law. They'll nitpick over what words exactly mean, or come up with tests on how to determine if something meets a definition, etc. And then other courts are expected to look up cases and remain consistent with their reasoning, or at least explain why they're interpreting something differently. It's more flexible, and tends to change over time. Sometimes if the courts are running into repeated problems, the legislature will then add further formal laws, or tweak the ones already there.

Case law is jurisprudence derived from English common law where judicial decisions and precedents established principles adopted as law. Written law as you call it is law established by statutes that have created a framework for governing and administering justice in our criminal and civil law systems. . Much common law has been codified into statute..

In plain English.

written law id legislated by government.

Case law is adjudicated by jury decisions.

Arguments based on precedents and those based on statutes.