What is the difference between embedded system and real-time system?

As a first incomplete answer I would say that real-time systems are an important subset of embedded systems. Generally speaking any real-time system is also an embedded system, as well as any RTOS is considered to be also an embedded OS.

Now, the second point would be to define an embedded system and afterwards to trace a line in between real-time systems and rest of embedded systems.

Embedded systems…. what are they? I read many columns and articles on the Internet claiming that it is more appropriate to say which “piece of computing” is NOT an embedded system.

Actually around 90% of microprocessors are manufactured for the embedded industry, so AMD and Intel cores found in our notebooks or desktops are just the tiny top part of the iceberg.

Clearly all kind of PC’s, ranging from desktops, to servers, to notebooks and so on, are not embedded systems. All of those are general purpose computers serve for browsing on the Internet, for audio/video streaming, for text editing, for performing sophisticated math computations and many, many different and complex tasks. Another thing which can be said about PC is that they rarely interact with the environment, usually they receive inputs from the user, via the keyboard, or from another computer via a LAN card.