Reading the link you provided, I find this sentence:
TUIs display computer graphics in text mode. An advanced TUI may, like GUIs, use the entire screen area and accept mouse and other inputs.
And there are some screenshots too, for example of Midnight Commander.
The difference of the definitions is that a TUI is a customized interface with hotkey and mouse inputs, not a shell where you enter a command line, (a command line interface), for example
bash, which is used in Ubuntu.
But both are text based interfaces, that need no graphical desktop environment or window manager.