Green Onions -> Also known as spring onions, these are onions or shallots too immature to have bulbs or Welsh onions that never get bulbs.
Scallions -> Immature onions without the bulb or Shallots used as green onions.
Shallots -> A medium sized allium with a milder flavor than regular onions. Sometimes picked young to use as green onions.
I'm surprised you're liking Truss's book. Language Hat's post on Louis Menand's review was enough to scare me away. She sounds like a prescriptivist nut who's not even very good at writing like a prescriptivist.
I'm still only a third or so of the way through, so we'll see. I think I know why I disagree with that assessment, but I'll post about it when I finish the book.