If I understand what you are asking, there are 5 or 6 types/categories of operating systems.
1. Single user - single task (SUST)- This operating system only allows one program/task to be executed at a time. An example of a single user - single task operating system is the old Microsoft Disk Operating System (MSDOS).
2. Batch - This type could be considered a subset of SUST operating systems. I think it is separate though, as it significantly predates what most people consider SUST operating systems. It is what used to be the norm for main frame computer operation. I think it is almost abandoned now. In a batch operating system, you can run a single job at a time. The job is normally broken up into multiple steps where each task executes a single program. Jobs are submitted via console commands or via job streams that are loaded by paper tape, card deck, magnetic tape, or have been previously stored onto disk allowing console submission.
3. Single user - multiple tasks (SUMT) - This operating system was a significant improvement in overall computer efficiency as it introduced queuing, scheduling, and interrupts especially of data requests from peripherals. This operating system would allow multiple programs to run concurrently by using time slicing. If a program did not perform any input-output operations (IO) the program could run for x number of microseconds before being forced out of execution, and an entry would be made to the scheduler queue indicating the program was ready for execution. At any IO, the program would be forced out of execution. The scheduler would keep track of the next program to enter execution (may be priority based). When a program was forced out of execution the scheduler would tell the program to load the next program ready for execution and that had reached the top of the scheduler queue. Interrupts told the scheduler when an IO was finished so it could be added to the scheduler queue. An example of a SUMT is Windows 3.0, 3.1, and 95.
4. Multi user - single/multi task (MUMT), this is also called time sharing. It functions much as SUMT except instead of just providing time slices for a programs on the scheduling queue, it provides time slices for multiple users each of which may have submitted one or more programs for execution. An example of MUMT is a the computer system at your school, library, or possibly even your home depending on how it is configured.
5. Real time operating system - sometimes called RTOS. These operating systems are mostly used for controlling machinery. Currently most are fairly primitive as they do not have to consider all the ways a user can input or request information. They perform a limited number of tasks extremely well. Where there are user/customer interfaces they are often handled by another system or tend to use console formats. The programs run by a RTOS constantly scan for new inputs from its sensors and takes appropriate action. Examples of computers that use real time operating system are those in your car, satellites, weapon systems like missiles, laboratory equipment, or the router for your connection to the internet. The new driver-less cars like those being developed by Google will have very sophisticated RTOS.
6. Multi processor operating system (MPOS) - this operating system supports multiple CPUs. This allows multiple tasks to be in execution at the same time. The SUMT and MUMT may appear to be executing multiple programs at the same time but in truth only a single program can be in execution at a time for any processor. Since MPOS has more than one processor, it can provide a performance improvement as long as two or more of the programs in execution are not awaiting IO.