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.