By "shows up in my module text" I assume that you mean it shows up in the module's action menu. Here are several tips:
1. The normal convention is to name the settings control "Settings.ascx" and it's codefile "Settings.ascx.vb" rather than "Setting" (without the 's'). Although the control can be given different names, what is critical is . . .
2. That the control be given a key of "Settings" in the module definition. This allows it to be found and appended at the end of the core provided module settings page.
3. Although you can use a control type of "Edit", I generally use "Admin". This seems to be the usual convention in most modules. However, I have seen "Edit" used in some. The control type is what governs its visibility to users in various roles. With a type of "Edit" it would be visible to anyone with Edit privileges. With type of "Admin" it is visible only to those in the Administrators role (including the superuser account "host" (usually).
4. To answer your other question concerning the difference between ModuleSettings and TabModuleSettings: The first is keyed on the ModuleID while the second is keyed on TabModuleId. Each instance of a module is given a unique TabModuleId, even if it is a copy of another module and even if it is added to the page using "Add Existing Module" rather than "Add New Module". Let's say that you first add your custom module to the portal using "Add New Module". It will be assigned both a ModuleId and a TabModuleId. Next, you add a "copy" of this module using "Add Existing Module". This second module will have the same ModuleId as the first, but a different TabModuleId. So, TabModuleSettings, which are most often used for display preferences, apply separately to each instance of a module, even if it is a copy while ModuleSettings are somewhat more global in nature applying to the original instance of the module in the portal AND any copies of that module. The DNN core does not provide a standard way of defining settings that would apply across all instances of a module instance regardless of the way in which it was added to the page.
If, after changing the module definition to reflect a control type of "Settings" for your settings control, you are still having problems, please post your Settings.ascx markup.