The correct distinction between private law and public law is that private law governs the relationships between individual citizens, covering areas such as contracts, property, and family law. Public law, on the other hand, governs the relationships between individuals and the state, covering areas such as constitutional law, administrative law, and criminal law. This distinction is fundamental in understanding how different areas of law are categorized and applied. 

Key Point: The distinction between private and public law is crucial for understanding the scope and application of different legal principles within the English legal system.