Yes you are installing grub on the boot MBR when you run "grub-install /dev/ sdwhatever. This is where grub belongs.

There is a partition somewhere on your box that has the actual grub files. This is where you are running the command "grub-install" from.

I find this very handy on my box as I have 4 drives. I can swap the boot/root (the OS with the files running the MBR) around to suit my needs and whims.