What is the name of the OS?

[kolla]

The GUI was Workbench.

The GUI was Intuition, Workbench is the graphical shell, or desktop as it is known as today.

[kolla]

But the actual Graphical User Interface we used to interact with the Amiga was Workbench.

Nope, the GUI you used to interact with the Amiga was Intution. The graphical shell, offered by the OS, was Workbench, and there were others, like Directory Opus, ScalOS etc. And they all use the same GUI, which is Intuition. It is Intuition that gives you multiple screens, windows, menus etc. that constitutes the amiga GUI - NOT Workbench. AmigaOS has a fully functional GUI also without Workbench.

I'd say that Workbench is similar to the Windows GUI and Intuition is similar to the Windows API that is used to enable Windows.

You are equally confused here, I see. :hammer:

[kolla]

I don't consider a set of function calls an interface.  You do..

No, you are confused over terminology, that's all. Yes, a set of functions can also be an interface, that's what the I in API is - application programming interface.

Let's just say we disagree on this point..

There is nothing to disagree on, the GUI is Intuition and the graphical shell provided by the OS is Workbench. That is not something to disagree with, it's just how it is.