Real Time System itself means the system working in REAL (present) time.
Real time system itself is not clear. Either it is Real Time Operating system (RTOS) or real time control system.
" A real-time operating system (RTOS) is an operating system (OS) intended to serve real-time application requests. " (WIKIpedia)
In a Real-Time System the correctness of the system behavior depends not only on the logical results of the computations, but also on the physical instant at which these results are produced.
Embedded System:
An embedded system is a computer system designed to do one or a few dedicated and/or specific functions often with real-time computing constraints. It is embedded as part of a complete device often including hardware and mechanical parts.(wikipedia)
OR
An EMBEDDED SYSTEM is a specialized computer system that is part of a larger system or machine. Typically, an embedded system is housed on a single microprocessor board with the programs stored in ROM. Virtually all appliances that have a digital interface, as watches, microwaves, VCRs, cars, utilize embedded systems. Some embedded systems include an operating system, but many are so specialized that the entire logic can be implemented as a single program.