I don't agree with that. I first heard CUI used to describe software like the Turbo Pascal IDE. I believe that "CUI" came about when GUI was coined to describe the modern graphical interface like Windows and Macintosh. That was in the latter 80s and early 90s. I've never heard TUI until literally today.

Additionally, TUI is either Text or Terminal User Interface. Either way, it seems to be heavily associated with ncurses. As I understand it, ncurses essentially outputs a stream, which includes things like ANSI escape sequences for position and color. By contrast, CUIs like Turbo Pascal wrote directly to video memory.

It’s true that TUI is a newer term than GUI and CUI. However, it isn’t exactly a new term either, its Wikipedia page was created in 2004. Look at the screenshots for illustration of what is considered a TUI: https://en.wikipedia.org/wiki/Text-based_user_interface

Or here some usage of the term in 2002 referring to a Turbo Vision or Norton Commander-like interface: https://www.digitalmars.com/d/archives/c++/dos/75.html

The technical means of how the contents of the TUI is established (character stream with special codes, or direct writes to text-mode video buffer) is largely irrelevant for the term. The essential characteristic is that the visual “state space” of the interface is a character matrix, and that the program treats it as such (instead of just unidirectional line-based output).

Maybe you are right that CUI actually doesn’t cover CLI. The Unix System V documentation uses “Character User Interface” for curses-based interfaces (https://books.google.com/books?hl=en&id=idAmAAAAMAAJ). Then CUI and TUI are roughly synonymous, though TUI is the widespread term nowadays.