What is the difference between public and private law?

Public law is an umbrella term. It includes different types of law: e.g., constitutional, criminal, administrative. The thing that they have in common is that they are all concerned with the relationship between individuals and the State. For example, criminal prosecutions take place for murder, because the State considers murder to be abhorrent and wishes to punish individuals who commit murder.

Private law is also an overarching umbrella, but includes other types of law: e.g., contract, tort and company. The thing that they have in common is that they are all concerned with the relationships that exist between individuals. For example, contractual disputes may be settled in court, because the individuals who signed up to the contract disagree over the obligations and rights owed to each other.