Module Library: the library classes are visible only in this module and the library information is recorded in the module .iml file.
Project Library: the library classes are visible within the project and the library information is recorded in the project .ipr file or in .idea/libraries.
Global Library: the library information is recorded in the applicationLibraries.xml file into the ~/.IntelliJIdea/config/options directory. Global libraries are similar to project libraries, but are visible for the different projects.