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.