TabModuleSettings are those that apply to EACH specific instance of a module regardless of whether the module instance was created by the "Add New Module" or "Add Existing Module" (shadow module) commands or by checking the "Display Module on All Pages" checkbox under the module settings advanced page.

ModuleSettings are those that apply "globally" to ALL instances of a module that has been created by the "Add Existing Module" command or by checking the "Display Module on All Pages" checkbox.

The DNN core does not provide for module settings which are truly global apply to all instances of a module regardless of how it was created.  For this purpose, some developers have used the ModuleID of the Host Settings module (which can have only one instance).  As I have often have need of truly global module settings (typically for non-DNN database connection strings and administrative settings), I added this functionality (tied to DesktopModulefID) to my own base classes (derived from PortalModuleBase, ModuleController, and ModuleSettingsBase) and added the table DesktopModuleSettings and the various stored proceedures that follow the same pattern as those used for the core's ModuleSettings and TabModuleSettings. Using these derived base classes, one can save settings that are tied to the TabModuleID (TabModuleSettings), ModuleID (ModuleSettings) or DesktopModuleID (DesktopModuleSettings) then retrieve them in the module controls from the Settings hashtable.  I would like to see the core add a similar, more global module settings capability in future releases.