there are two different kind of Settings: ModuleSettings and TabModuleSettings. And then there is the content.
The title of a module is a TabModuleSetting ("Tab" is or was the original name for page), so for each instance of the same module (on different pages) it is possible to change the title. A ModuleSetting is the same for all instances of the module, and so is the content.
Hope that explains it.
If you want to change the title on all pages, uncheck the "Display on all pages" checkbox on the original page (the Home page in your case), save the settings, change the title, save, and then check the checkbox again (and save). The original title is always copied to the module instance on other pages at the first moment.