Law of the sea
The Sea
Law of the Sea is "A comprehensive body of international law governing all human activities on the ocean." While it has a long developmental history it is, generally speaking today, codified in the United Nations Convention on the Law of the Sea (UNCLOS), which also reflects customary international law.
While its purpose is to record the legal framework for activities like navigation, marine resource use, protection, and jurisdiction over maritime zones providing a formal, established legal rules that nation states should follow in the maritime environment, because limitations of the code it continues to rely upon other components and principles that are not law.
Equity
Equity is a component or principle within the broader framework of the law of the sea, and not a separate system. It judicially informs and guides the application of the law of the sea to achieve a reasonably just result.
Therefore, the law of the sea provides the established rules for oceans, while equity is a principle and tool used within the law of the sea, particularly for maritime delimitation, to ensure fair and just outcomes when strict rules lead to unfair results. While the law of the sea is the foundational legal framework for ocean activities, equity offers judges and arbitrators a margin of appreciation to modulate these rules and achieve "equitable solutions" in areas like the Exclusive Economic Zone, reflecting the needs of various states in a balanced way.
Civil
Law of the Sea is a specialized branch of public international law that applies to nation states in their interactions on the ocean and is distinct from Civil law which is commonly a broad legal system, which also distinct from common law, that focuses on private rights and obligation for governing private relationships within a country's domestic jurisdiction including disputes between private individuals and corporations.
Common
Common Law is "A body of law based on judicial decisions, or precedents, from previous court cases." Those judicial decisions were the product of the Jury within the law of the land of England before the king's courts after 1066.
Theories
Because Civil law is a body of rules established by men, often through their legislative bodies, we will find equity used again as a system of principles developed in these courts of law to ensure fairness and provide remedies where the civil law is found to be inadequate. So in both the Law of the Sea and in the Civil law we will see the principals of Equity present in the operation of both systems leading to considerable confusion in the establishment of many legal theories.