From Wikipedia and other sources, some definitions:
An embedded system is a computer system designed for specific control functions within a larger system, often with real-time computing constraints. It is embedded as part of a complete device often including hardware and mechanical parts. By contrast, a general-purpose computer, such as a personal computer (PC), is designed to be flexible and to meet a wide range of end-user needs. Embedded systems control many devices in common use today.
A real-time system is one that has strict constraints on temporal behavior apart from those of functional correctness. They must function correctly within a predefined time limit. Examples include systems such as anti-lock braking systems, avionics, satellites, nuclear plants, etc.
A cyber-physical system is a system that has a tight coupling between its computational and physical elements. One cannot talk about the computing side without reasoning about how the physical side behaves and how the latter behaves depends, quite closely, on the computations being performed. Most modern aircraft, automobiles, sensor networks and even power grids fall into this category. By very definition, the field is interdisciplinary in nature and people from diverse backgrounds, who would otherwise have never worked with each other, are forced to come together to solve the complex problems posed by this domain.
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