A more thorough explanation:

The Law of Nature and Nations is also known as International Law. It is a legal system that governs the relationships between nations, international organizations, and individuals. It includes the law of international relations and covers topics such as human rights and war crimes.

Customary international law is one of the principal sources of the international legal system. It derives from the practice of states and is accepted by them as legally binding.

Private international law, also known as international conflict of laws, deals with disputes of a private nature, even if one of the parties is a private state. It is a part of each legal system's private law.

For example, if a person from one country gets into a car accident in another country, private international law would determine which country's laws apply to the case. This illustrates how private international law regulates disputes of a private nature.