I found a description somewhere on the net, which says: ''Projected (2D): Its effect won't depend on the mesh, but on the point of view which you're looking at the mesh.''. What does it mean? What is a difference between this mode and a simple proportional editing mode (which you enable using the O button)? Tried to compare them, but with no different results.
To explain it, here's an example of Connected mode. I'm pulling one vertex on the right side view of the image. Notice the effect on the left screen: it works like the standard mode for proportional editing, the vertices within the influence circle will be transformed proportionally.