For my first feature I was the editor and then a friend of mine at Universal put together a sound team for all the post sound. From what I understood he had a couple guys going through all the dialog and cleaning up the edits between each cut, making sure there was no yelling from off camera from crew, stuff like that which is missed sometimes in the edit, placing in ADR and identifying sections that needed it -- That was the dialog editing from what I could tell.
They also placed in all the background sounds like wind, birds, ambient nature sounds, insects, etc. (it was a western) as well as any foley work such as bottles clinking or chairs moving, drinks being poured, punches and kicks, gun shots, etc. -- I believe this was more of the Sound Editing.
We then also had Sound mixers who took all of the work the Sound/Dialog editors did and mixed the levels and speaker placement (stereo or 5.1).
But as Kim was saying, on a small project you will likely have an editor doing all of these theirself. Just make sure you are familiar with what an M&E track is, that is important for if you are trying to get distribution.