Feel rather not satisfied being not really crystal clear on how is the grub working mechanism
It has syntax (in its help)
Usage:
grub-install [OPTION...] [OPTION] [INSTALL_DEVICE]
As we know working on main storage, referenced by/dev/sda having its sub/child, is usually most common/simplest device: main HDD,
How/what actually INSTALL_DEVICE best suited here, /dev/sda or its sub., e.g. dev/sda7, i.e. how each works different, and even further how's grub work if no INSTALL_DEVICE given at all as indeed it's optional