There's a trouble with terminology that I would like to clarify.
Linux kernel (probably all UNIX kernels?) executes in supervisor mode (aka kernel mode), whereas user applications run in user mode; each mode has also its own memory space.
Unix transfers execution from user mode (user space) to kernel mode (kernel space) when application issues syscall or is interrupted by hardware interrupts.
However, most of technical literature talks about context switching, when the kernel switches execution from one task (process) to another.
How is called exec transfer from user mode to kernel, and how is this related to the context switching?