Private law is that part of a legal system which is part of the jus commune that involves relationships between individuals such as the law of contract or torts as it is called in the common law and the law of obligations as it is called in civilian legal systems. It is to be distinguished from public law which deals with relationships between natural and artificial persons (i.e., individuals, business entities, non-profit organizations) and the state including regulatory statutes. penal law and other law that effects the public order.
Public law is the state v someone, but private law is person v person and has nothing to do with government
See also: civil law.