update-grub

This command is an alias for grub-mkconfig --output /boot/grub/grub.cfg.
View documentation for the original command

$ tldr grub-mkconfig

update-grub

update-grub is a convenience wrapper that generates a new GRUB configuration file. It is equivalent to running grub-mkconfig -o /boot/grub/grub.cfg and is commonly found on Debian-based distributions.
The command reads configuration from /etc/default/grub and scripts in /etc/grub.d/ to generate the bootloader configuration.

Requires root privileges. The actual path may vary (/boot/grub2/grub.cfg on some systems). Always review changes to GRUB configuration carefully.

grub-mkconfig(8), grub-install(8)