CUI was me messing up. I meant TUI (text user interface).

The command line interface (CLI) is the original TUI and is always prompt and response. You're prompted for a command, you type it in and then the computer spits out the answer below.

The original CLI were printed on a teletype machine before there were videoterminals. So if your TUI has a real typewriter-kind-of-experience, that's a CLI. So even something like cowsay is CLI.

TUI is a more broadly encompassing term. This includes CLI, but also programs that display text or text like lines all over the screen. The popular library ncurses is generally used to make these programs. Popular examples would be vim, or emacs, or htop, things like that.

A very simple example of a non-CLI TUI program is less. It lets you pipe output of a CLI command into it so that it can be scrolled without using only the screen buffer.

[Edit] "Console" is a pretty unique term. Back when a computer took up an entire room, the console was the table that the computer operator sat at. Some of the earliest WWII era computers, a console might have just had a panel with indicator lights and you primarily interacted with the punchcard interface.

But eventually, the teletype machine or videoterminal sat on the console table. So doing something "at the console" became slang for using CLI and the terms began to be used interchangeably.

And if you want to go deeper into the weeds, there are still console table furniture you can buy for non-computer usages. Basically a console table is a kind of narrow side table you find near a door. Originally most of these tables included front legs made of "consoles" which is an ancient greek corbel (architecture element) that is shaped like a scroll.