Try using stop on that( System Idle) you will notice that you can't stop system process that easy!!!
And for yours question when you hit End task it closes program that is running including his process, but some processes (particals of some programs) can run without whole program and you can identify them by name check here:
http://www.what-process.com/index.aspx so process can be part of task(program) or whole (task) program !!!