Modules can save settings "per instance" or "per tab instance" and that is partially how it determines that.  What this means is if you use "ModuleId" and in the module settings area UpdateTabModuleSetting then if you copy a module from tab 'x' to tab 'y', they will be able to have completely different settings but similar structure; taking this a step deeper, if you save data for a module using ModuleId, then the data in module from tab 'x' will be visible in tab 'y', but again, you could change the structure based on whatever module settings you have.  Now, if you just use ModuleId for everything, then a module from tab 'x' copied into tab 'y' will be EXACTLY the same, essentially a carbon copy.  Whenever you change settings in any of the instances it will change them for every copy.

The way you copy modules to other tabs is "add existing module" from the control panel instead of "add new module". 

So in a nutshell:

• TabModuleId -- use when you may copy the module from another page, but want to have it distinct in certain functions (whether UI, placement, etc)
• ModuleId -- generally what you will use in most cases; keeps copies of modules consistent