5.3 What are all those names like slink, potato, etc.?

They are just "codenames". When a Debian distribution is in the development stage, it has no version number but a codename. The purpose of these codenames is to make easier the mirroring of the Debian distributions (if a real directory like unstable suddenly changed its name to stable, a lot of stuff would have to be needlessly downloaded again).

Currently, stable is a symbolic link to sarge (i.e. Debian GNU/Linux 3.1) and testing is a symbolic link to etch. This means that sarge is the current stable distribution and etch is the current testing distribution.

unstable is a permanent symbolic link to sid, as sid is always the unstable distribution (see What about "sid"?, Section 5.4).