I think you're overcomplicating this; the meaning of these words is in the acronyms themselves. What's a UI? A user interface -- any layer that goes between the user and some machine. What's a GUI? A user interface that is graphical, or: a layer that uses graphics to go between the user and a machine. Since websites use graphics (pixels, on a screen), and they sit between the user and a computer, they are GUIs.