International is a rather open-ended term, while intergovernmental specifically refers to the fact that the participating parties or members are sovereign states and intergovernmental organizations.
As a result, only intergovernmental universities are subjects of international law.
The designation “international university” (category regional/international in the ‘List of Universities of the World’) is applied by the International Association of Universities:[1] About 10 other public institutions established under international law have been identified as established under international law, for example the University for Peace (Costa Rica), Ecole Supérieure Multinationale des Télécommunications (Senegal), and the Eastern and Southern African Management Institute.
He notes that there is no main campus and that several national entities fund and own the institutions.
Examples of institutions using the actual name International University are: Two well-known international university networks (private) are Alma Mater Europaea of the European Academy of Sciences and Arts, and Laureate International Universities.