what is the meaning of “Equidistance line; equidistant line; median line” in law of the sea, LOSC and customary international law

In UNCLOS analysis, an “equidistance line,” synonymous with “equidistant line” or “median line,” means a line every point of which is equally distant from the nearest points on the baselines of two States.

Comment
UNCLOS Article 15 uses the term “equidistant,” but the definition has been more broadly stated to take into account agreements contemplated by, e.g., UNCLOS Articles 74, 83 or 134(4), or Shelf Convention Articles 6(1), 6(2). In LOAC-governed situations under the “other rules of international law” clauses in UNCLOS, a different definition may apply. The same may be the situation if the UN Charter supersedes UNCLOS or if jus cogens norms apply.
Consolidated Glossary ¶¶ 31, 59 define “equidistance line” or “median line” as a “line every point of which is equidistant from the nearest points of two States.” Former Glossary ¶¶ 29, 51 define “equidistance line” or “median line” as a “line every point of which is equidistant from the nearest points on the baselines of two or more States between which it lies.”
UNCLOS Article 15 inter alia provides that when two States’ coasts are opposite or adjacent to each other, unless there is an agreement between them, neither State may extend its territorial sea “beyond the median line every point of which is equidistant from the nearest points on the baselines” from which the territorial sea’s breadth is measured. Territorial Sea Convention Article 12(1) recites the same formula, omitting the agreement exception. Shelf Convention Articles 6(1) and 6(2) have the same formula as in UNCLOS Article 15, but the analogous UNCLOS continental shelf and EEZ provisions, UNCLOS Articles 74, 83 and 134(4), do not.