To furter complicate your question:
There is also a TabsModuleSettings table which I believe is used to configure a instance of your module on a particular tab therefore I would say the real shared setting values you are looking for are maybe in these 3 tables:

•  DesktopModules
•  ModuleDefinitions
•  ModuleControls

(not sure anyway)

I am sorry, but not of you won the prize 

The correct answer is:

when you place a module on a page using "add new module" in the control panel, a new module instance is created as an entry in Modules table, which holds the content. Same time a page reference is created to link the module instance with it's display and location on a page, by adding an entry in TabModules table. Why this? Because this allows to share content: if you select "copy existing module" in the control panel (which is misnamed and should be named "create shadow copy"), only an additional entry in tabModules table is created, pointing to the same module instance (entry in modules table), resulting in an update of the module content on both pages.

ModuleSettings contains settings for the module instance, TabModuleSettings holds settings for each specific reference only. E.g. UDT uses modulesettings for column setup properties (some are in custom table) and tabmodulesettings for output specification like rendering options, which allows you to have different display of the same content on different pages.

PS: module developers and admin need to be aware, that tabmodulesettings are not contained in module exports by design.