Is the Ubuntu GUI a TTY by itself?

Is it accurate to name the Ubuntu GUI (or any other operating system GUI) a "TTY" for that matter?

A desktop needs a tty to run but that does not make the GUI a tty. You should call it a session and a tty you use to login either to command line session or a desktop session.

Is it true to say that any Window (like a directory window or a gedit/geany window) is a TTY by itself or just a (window) part of the larger GUI TTY?

No. Those are processes (within a session).

TTY really is an instance of virtual terminal. Early computers were just giant boxes, to which a real, physical terminal was connected and are generally called TTY (short for teletype). Virtual terminals are called virtual for that exact reason - your computer is now one single unit, and you have couple different virtual software teletypes (more specifically, for Ubuntu it's 6 ttys, but you can spawn more. See my answer here: https://askubuntu.com/a/817859/295286). Within TTY you can run processes, be it a text-based shell like bash or graphical server within which runs a graphical shell.

What happens precisely is that you have specific instance of GUI running ( or in more technical terms, you have X11 server running ) in a particular tty. In case of Ubuntu, it defaults to TTY #7. When I was using Fedora 21, that defaults to TTY1. And you can have multiple instances of GUI, see this for example: Start another GUI on different TTY

So effectivelly, GUI session is nothing more than a separate process running within a TTY.

Additional info:

• https://askubuntu.com/a/481915/295286
• https://unix.stackexchange.com/q/359038/85039

A desktop runs on a TTY. A window is a different process, non-TTY related. It just shows in the desktop environment.