Add-ons (also spelt addons) are python scripts that can be used just by "installing" them (which literally just copies it into the right folder).
As far as I know, there is no such thing as a plug-in (or plugin) for blender, but it's a common term that's sometimes used instead of add-on, but means the same thing.
Builds are needed when there are actual changes to blender's source code (not just something like an add-on you can plug in ;) ). Often blender's python API doesn't give you enough access to perform the function you need, or is too slow, and thus you need to implement the function directly in the source code and re-compile blender. Compiling blender can be a bit of a bitch, so the dev (or some smart person) will compile it for you and upload the new compiled code (the 'build') somewhere for regular humans to use (graphicall.org usually)
Some more info:
- Quick overview and introduction to the python API
- A bit more in-depth overview of the Python API
- Where to get add-ons
- Docs for building blender yourself: Windows, Linux, Mac
