As Private Law, often called Civil Law, an area of Law is specified which governs the legal relations between citizens respectively legal persons (such as registered associations, Limited Liability Companies, Joint Stock Corporations, etc.). The entities involved (natural or legal persons) have the same legal status before the law, i.e. both parties are on the same level respectively are equally established by law.
So here argue citizens vs. citizens and not the State vs. citizens as in Public Law or in Criminal Law.