Just going over my school notes, my teacher identifies multi-tasking OS, and time-sharing OS as two different things.
I really don't see a difference between the two.
MULTI-TASKING: You load a number of programs in the memory and execute them. You execute another program if the time quantum allocated to the current program expires OR if it goes on to do I/O and leaves the CPU OR if it finishes execution.
TIME-SHARING: the same,again.
The same applies in case of serial processing and batch processing. Although they are the same, I guess the only difference would be the way in which control information is passed to the CPU. Maybe, and again MAYBE, in serial processing you need to provide the punch cards with all the processes while in batch, the entire batch uses the same set of control information.
Like all the print jobs would have the same control information.