The distinction is - if it runs over ssh (no x / graphics login) or on a headless machine - TUI
If it requires graphics login, even if it uses character layouts - GUI
IMHO the T/G is not for the display elements, it's for the type of session.
Not to put too fine a point on it, but X11 runs over ssh just fine. No "graphics login" required.
Not to put too fine a point on it, but X11 runs over ssh just fine. No "graphics login" required.