They are simply codenames for different versions of XBMC.
XBMC 12, a.k.a. under the codename 'Frodo', is the latest stable version of XBMC.
The current version is 12.3, which is 12.0 plus loads of fixes that were backported from 13.0 development
XBMC 13, a.k.a. under the codename 'Gotham', is the upcoming new version of XBMC which is currently in development, and has not yet been released as a final version.
There were monthly alpha versions done up until recently when we went into feature freeze. This means no new features will be added, and only bugs fixed until we are ready to release a beta, release candidate and final. It also means that the
nightly builds should get more stable every day.
A list of important new features and functionality in Gotham can be found on the wiki under
XBMC_v13_(Gotham)_changelog (wiki)
Addons:
There are fewer API changes between 12 and 13 then there were between 11 and 12. This means that many/most of the 12.x addons actually work under 13.x
Currently the 13.0 releases use both
the frodo addons repo and
the gotham addon repo. Addons which only work in gotham should be in the gotham repo. Addons which work in both can have updates in the Frodo repo, or have seperate versions (one in frodo and one in gotham).