> But it's also common to use "CLI" to include "TUI" programs [...].

It is indeed common, and (IMO) it is harmful, as TUI programs are just GUI programs in disguise. They do have two unique strengths: readily accessible over a serial console or an SSH session; and being the lowest common denominator of GUI programming. But they don't share any of the typical (desirable) qualities of CLI programs; typically, any CLI features (if present at all) are an afterthought.

    $ ls | vim
    Vim: Warning: Input is not from a terminal