On the other hand, there are many elements in the user interface that are not text. In fact, I think it would be quite understandable if one even separated REPLs like bash or octave to be "text user interfaces" while applications that make use of character placement and border special characters "terminal user interfaces", because they use means beyond text stream to communicate with the user. One might even render straight up graphics to a terminal [emulator application].

Even X had a separate application called xterm 42 years ago: the complete X system was not to my knowledge called a terminal system, except perhaps when discussing the dedicated client devices, such as VT1300. Also the term "virtual terminal" as far as I know has always referred to a the kind of interface this application is making use of.

So I think we can just accept that the term is overloaded such that "terminal" refers to both of these situations, as there is no historical precedent to have it exclude the other situation, and the term "terminal-based application" is completely clear to a rational listener.