Private law applies to relationships between individuals in a legal system. e.g. contracts and labor laws. Public law applies to the relationship between an individual and the government. e.g. criminal law.
Private law governs relationships between individuals, such as contracts and the law of obligations. In countries where it is known as “common law,” it also includes contracts made between governments and individuals.
Public law is law governing the relationship between individuals (such as citizens and companies) and the state.
Private law includes civil law (such as contract law, law of torts and property law), labor law, commercial law, corporations law and competition law.
Public law includes constitutional law, administrative law and criminal law. Constitutional law considers the relationship between the state and the individual and between different branches of the state. Administrative law regulates bureaucratic managerial procedures and defines powers of administrative agencies. Criminal law involves that state imposing sanctions for defined crimes.
Smoking indoors is a classic example of public vs private law regulation. As a public law, smoking indoors is prohibited is certain countries. However, people formed membership clubs where the agreement between the member and the property owner is a private law which the government has no regulation over. Covered by this private law, the members are then allowed to smoke indoors.