grub-install is the standard GRUB tool, the official GRUB utility provided by GRUB itself.
It installs GRUB to a device and sets up bootloader files, - it does require very precise syntax and knowledge of your system’s boot setup.
So for example, you might use it this way:
sudo grub-install /dev/sda
It can be error-prone if you make a mistake, especially with UEFI systems.
install-grub is a Manjaro specific wrapper scriptj designed to greatly simplify GRUB installation. It wraps grub-install and automates some more complicated and error-prone steps…, reducing the PEBCAK factor and making GRUB installation more accessible:
Just typing sudo install-grub is all it needs. It’s especially loved by anyone restoring a GRUB from the live ISO or after system changes.
Obviously it’s also true that the noob friendly install-grub is a higher level tool, limited to more common cases… whereas grub-install is the sharper tool, requiring more system knowledge but coming also with more flexibility for advanced users.
So your answer is… YES, you can do the same job with grub-install ( and install-grub would not work without it either).