Sorry, but this 65 yo grey-beard disagrees. A TUI to me, back in the 80s/90s, was something that ran in the terminal and was almost always ncurses-based. This was back when I was still using ADM-3A serial terminals, none of that new-fangled PCs stuff.
We might've been caught on different parts of the wave. I checked Ngrams out of curiosity
https://books.google.com/ngrams/graph?content=TUI&year_start...
Basically it was never used, then it was heavily used, and then never used, and then in the early 00s it took off again.
That'd explain why you used it, I never did, and now young kids are.
Exactly. A CLI is a single line - like edlin. A TUI takes over all or most of the screen, like edit or vi or emacs.
Norton Commander (or Midnight Commander) is probably the quintessential example of a powerful TUI; it can do things that would be quite hard to replicate as easily in a CLI.