Linux – Why do we need the reboot function in different binaries

Check the Rosetta stone for Unix for ways to perform common administration tasks on various unix variants. When it comes to shutting the system down, most systems provide two commands: one that stops the system services cleanly (going throough a shutdown runlevel, on variants that have runlevels), and one that stops the world and reboots instantly (possibly without even unmounting filesystems cleanly). You should always try the clean variant first, and only use the instant variant if the clean variant failed; if you use the instant variant, first shut down as many things as you can manually.

I believe all the systems you list require proper arguments to shutdown to shut the system down cleanly and reboot. Check the shutdown(8) or shutdown(1m) manual page on each system.

A shutdown can fail only if one of the system services, the kernel or the hardware is buggy. Most OSes will forcibly shut the system down even if some system service fails to stop cleanly. If you have a kernel bug or hardware trouble (such as a misbehaving disk), it's possible for the shutdown process to fail. There isn't much recourse in that case: hardware failures often require physical intervention. A watchdog may help, if you need to reboot the system in case of a hardware failure.

The source code explains the difference as being how it handles the --help option.

  /* Recognize --help or --version, but only when invoked in the
     "[" form, when the last argument is not "]".  Use direct
     parsing, rather than parse_long_options, to avoid accepting
     abbreviations.  POSIX allows "[ --help" and "[ --version" to
     have the usual GNU behavior, but it requires "test --help"
     and "test --version" to exit silently with status 0.  */

Demonstrating

$ /usr/bin/test --help
$
$ /usr/bin/[ --help
Usage: test EXPRESSION
  or:  test
  or:  [ EXPRESSION ]
  or:  [ ]
  or:  [ OPTION
Exit with the status determined by EXPRESSION.
[...]

In the bash builtin version, the only difference is that [ requires ] at the end, as you said.