Interrupt handlers can be fast because they don’t have to save the entire hardware state; they only have to save registers they are planning to use.
But when an interrupt occurs, the kernel does not always resume the interrupted process. It has the option of switching to another process. This mechanism is called a “context switch”.
In general, the kernel doesn’t know which registers a process will use, so it has to save all of them. Also, when it switches to a new process, it might have to clear data stored in the memory management unit (see Section 3.6). And after the context switch, it might take some time for the new process to load data into the cache. For these reasons, context switches are relatively slow, on the order of thousands of cycles, or a few microseconds.
In a multi-tasking system, each process is allowed to run for a short period of time called a “time slice” or “quantum”. During a context switch, the kernel sets a hardware timer that causes an interrupt at the end of the time slice. When the interrupt occurs, the kernel can switch to another process or allow the interrupted process to resume. The part of the operating system that makes this decision is the “scheduler”.