Is it character mapped, designed to run in a tty terminal? TUI.

Is it pixel or vector mapped, designed to run in a graphics terminal? GUI.

Of course strictly speaking TUI is a subset of possible graphical user interfaces, but the term GUI was coined to denote interfaces other than the already-ubiquitous text terminal interfaces.

TUIs have since absorbed GUI interface elements like buttons, checkboxes, and even pointer input, which I think is causing the terminology complaint here. Classical TUIs like Norton Commander are more about keyboard input and navigation. But being text-mapped is the identifying feature of a TUI, I think most people accept.