Booting Slackware 15 .iso from VirtualBox brought me to a TUI shell, although "shell" in this case is "menu-driven with only the available options," so more of a running program, out of which exiting brought one to a CLI shell as root.
TUI to me also means "arbitrary coordinate rendering," i.e. something completely distinguishable to a command-line prompt (and line-editing). So one expects modal dialogs and popups, menus / menu navigation, and essentially "windows of experience."
TUI also may mean "cannot easily pipe things," because we have (x, y) positions instead of one cursor location receiving all inputs. The idea of improvised composability may be absent.
It would be neat to see an "expect for TUIs." I wonder how it would standardize the idea of "textual graphics" across a variety of different TUI tools.