I hear the term 'bolt-on' used in many contexts, specifically in my organization where PeopleSoft is used extensively. I don't know exactly how it differs from an 'extension' of an existing product, a new module within an application, or an 'add-on' like you would purchase for a product you own. Is there a more formal definition of 'bolt-on' that I'm not familiar with?
Most of those terms only have meaning in a specific context. In particular, I've only heard bolt on used with respect to PeopleSoft, where it means a separate application that integrates with the PeopleSoft ecosystem. Here's an article about the difference between bolt-ons and customizations (tl/dr: a customization is a change to some part of the PeopleSoft system, a bolt-on is a separate thing that uses the PeopleSoft system).
The other terms you used, module, extension, and add-on also need to be considered in a particular context. For example, in some contexts a module could be some source code component that needs to be compiled into a program, while in others it may just be a functional component of the program that can be added without modifying the original.
If you're unsure of what someone in your office means by a particular term, ask them. If you feel you can't do that without looking uneducated, check the documentation for the pieces of software that they're talking about.
As M. Dudley stated in a comment below the answer, "bolt-on" is used to identify a component that is quickly and easily added to another system. This distinguishes it from components that require more sophisticated integration or customization.
I would also add that this is mainly a slang term, and can also mean anything added to a system hastily, without regard for suitability or esthetics.