I would agree with you that the ones that don't fold up are better described as slicers than mandolines, but there are V-shaped mandolines being sold on amazon. Both types are being called "mandoline slicers" to add to the confusion!
My experience with mandolins has been that if you go to a local kitchen supply store (amateur or professional) you'll run across at least three separate price levels. We've always had luck with the mid-range mandolins, though they usually don't last for more than five years. We prefer going to a local store so we can actually eyeball the gizmo and handle it before deciding on it. To us at least it's the kind of item we're uncomfortable buying from an on-line description.