Depending on who you ask, embedded software runs on the following:

• A 4-bit microcontroller surrounded by some custom logic and no OS
• An Atom-based PC-104-sized card buried in the bowels of a machine with a real-time OS
• A network of small, custom boards controlling everything in an automobile, including the brakes, engine, transmission, infotainment system, AC and heating, headlights, wipers, radio, and navigation software
• A 64-bit, multicore AMD Ryzen monster with a GPU that makes a hardcore gamer jealous and costs more than the PC motherboard it is running on

Over the course of my career, I have worked on systems at both ends of the spectrum, and at several places in-between. All of these have qualified as an embedded system running embedded software.

Some embedded systems have no OS, while others may have full blown OSes, such as Windows...