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An embedded system is basically made to do one set of task or similar. An internet router uses an embedded system.
A Plc can also interface with an embedded system. There are some more cases where either will do. One commonly used appliance that would work with either is an automatic coffee maker. Also, clothes washing machines used to use simple Plc while many of the new ones use embedded systems.
PLC stands for programmable logic controller and had in old days its own simple PLC-language to control industrial peripheral. It is designed to be very flexible and has modular I/O modules which can be configured and expanded. Thus the I/O specification is around 24V and standardized. The typical tasks of a PLC will be automating a production process. As already said an embedded system is the core of a PLC. Usually a closed system(like the mentioned coffee machine) is not modular expandable. As "embedded microcontroller" indicates it inside the system with a fixed function. If you design with a PLC an automated process and is then a complete system, the PLC becomes "embedded".