Modules are used to extend or change core G3 behavior. There are two types of modules with in Gallery3:

Core: modules required in order to function properly.
Contributed: modules that extend the functionality of the basic gallery3 product. 

The real difference between the two types is who supports and is responsible for them.

The core team is responsible for maintaining core and optional modules. There are coding and documentation standards that must be met for general release. Changes to the core modules have a stringent review process in place to insure that any changes provide a high quality product with know impact of current and future installations.

For Contributed modules, the community is responsible for the maintenance of these modules. This is not to say a core team member may develop and assist in the enhancing a contributed module, but they are not part of the core product. The core team does not require or enforce standards and using the review process is optional. These are truly a case of use at your own risk.

This listing does not include modules and/or themes that are only available via the Gallery 3 forums and which don't have a corresponding codex page.