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Real time operating system means that the system responds in real time or in present time for example when we type some thing using keyboard  the system respond without any delay and show what is typed on screen

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Real time system means that the system is subjected to real time, i.e., response should be guaranteed within a specified timing constraint or system should meet the specified deadline. For example: flight control system, real time monitors etc.

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A real-time operating system (RTOS) is an operating system (OS) intended to serve real-time applications that process data as it comes in, typically without buffer delays. Processing time requirements (including any OS delay) are measured in tenths of seconds or shorter increments of time. A real time system is a time bound system which has well defined fixed time constraints. Processing must be done within the defined constraints or the system will fail. They either are event driven or time sharing. Event driven systems switch between tasks based on their priorities while time sharing systems switch the task based on clock interrupts. Most RTOS’s use a pre-emptive scheduling algorithm.

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Realtime OS: Realtime Operating System refers to serve realtime application that usually process data without any time delay. It provides an instant response to the client, after execution of information from server. It switches between tasks, giving the impression that multiple programs are being executed at the same time. The response time of Realtime Operating System to external events. When switching between Tasks the RTOS has to choose the most appropriate task to load next.

To provide a responsive system most RTOS’s use a pre-emptive scheduling algorithm. Real-time operating systems are often required in small embedded operating systems that are packaged as part of micro devices.

An RTOS has an advanced algorithm for scheduling. Scheduler flexibility enables a wider, computer-system orchestration of process priorities, but a real-time OS is more frequently dedicated to a narrow set of applications.