fwiw, i've always used 'init 0' to shut down all sorts of unix/linux systems.
In EL7/EL8, init is now a symlink as well because everything is controlled by systemd.
On old school unix, and I think even early Linux, halt was an /immediate/ halt, as in catch fire. might as well hit the power switch.
Not quite. Shutdown is a timed thing so you can tell it to shutdown or reboot at a certain time or after a certain delay and it can broadcast messages to the users - it's useful on multi-user systems to be able to warn users that the system is about to go down. Halt is an immediate thing without any broadcast messages or delay but it does do the halt cleanly. There is an option to halt to not sync the disks - this is not a wise thing to do and is an emergency option - certainly the original man pages for halt said something like "only do this if your disks are on fire".
P.