What is the correct way to turn off a Unix/Linux server?

From my googling, I have learned (hopefully) the following:

shutdown: I should use this, with the parameter -h to halt, or the parameter -r to reboot

halt: halts the computer (stops the processor? does this physically turn the power of the computer off?). I think this will call shutdown if not at init0, otherwise just halts.

reboot: if not at init6, calls shutdown, otherwise just reboots the computer.

if all that is correct, then the only thing I can't figure out is what exactly 'halt' does. Does it just stop the processor but not turn the computer physically off? How do I "poweroff" the computer?

Thanks