So, that's really it? Both Wikipedia and the dictionary I use weren't being clear, talking about attic space, entire rooms being a loft, or there being lofts within lofts... with that last one being accompanied by words like "confusing" and "sometimes," which makes me want to find a better way of referring to it. Aside from "upper open loft area," which is a bit of a train wreck.
Maybe I should make up my own word for it. Something inspired by hayloft, which is short, apt and doesn't leave any room for ambiguity, like using loft could create: "Go to the loft? I thought that's where we were?"