What is the relationship between common law rights and statute?

Statute law refers to the laws that have been passed by the legislature and have been written down and 'codified' for use.

Common law refers to the laws that are more or less "that's the way it has always been done." Common law relies upon the body of history and prior cases to establish what the rules are, one of the reasons lawyers study past cases so much.

Some states have not codified murder, as the common law definition is more than adequate.