HMI and SCADA system

I think the SCADA part you know but, the confusion is the HMI part.
HMI stands for Human Machine Interface and HMI is a term and not an application.
HMI is the communication/interaction layer between the user and the process.
In the process industry the "Human" is the operator and the "Machine" is the process control data and instruments. HMI is not a term exclusively used for processes but you can find the HMI in any system.

Example:
when you have Music on your computer and you want to listen to that Music you will start a Music player. That player is the HMI, you can now play, pause, go forward or backward and stop the Music. With the Music Player you can interact with the Music files stored on your computer.

So, HMI is the interaction part of the SCADA system.

However, the issue that blurs that otherwise clear line is the introduction of units that have integrated all the functionalities that we used to have clearly defined and separated (HMI, PLC, SCADA, DCs etc.).

A touch-screen these days, f.ex., is not "only" a touch-screen – it has extensive programming capabilities, as well as I/Os, essentially eliminating the need for a dedicated controller or a SCADA-system (to some extend).

In my opinion, we need to review our definitions of these terms. As you said, HMI is what the operator interacts with to make something happen (touch-screen, push-buttons, levers w/e). But when you integrate functionalities that are usually handled by a controller (control-loop, I/Os etc.), it becomes more than a simple HMI.

Let's take another example:

Your desktop has a cabinet that runs all your applications; to interface the computer, you have a keyboard, mouse and monitor. Without those, the computer is still running, but you cannot interact with it.

A laptop, however, is another matter; the keyboard, mouse and monitor are integrated, and you cannot disconnect them, without turning off the whole computer. It's still the same architecture as the desktop, and it functions the exact same way, only the HMI is now an integrated part of the whole package.

As professionals, few of us have any problems identifying the two "layers" from one another, but for non-professionals, it can be confusing, and understandably so, since technological advances has made it possible to integrate more and more functionalities into less physical space, allowing every gadget to have a screen and endless possibilities (software-wise).

To re-cap: HMI is what makes an operator capable of interacting with an underlying entity; the HMI can have many forms, be integrated into other devices or be a standalone device. It can not, however, function on its own, without a connection to the underlying entity. The underlying entity can function without the HMI.

A SCADA system has a HMI, but it's not a HMI in itself; SCADA is more of a communication-entity linked to various controllers.