Definition

In most OS running the systemd init subsystem, all legacy power management programs are symbolic links to systemctl subcommands to preserve backward compatibility.

Linux Systemctl Power

systemctl reboot — reboot systemctl poweroff/systemctl shutdown — shutdown systemctl halt — shuts down the system, stopping all services and processes and unmounting the file system, but leaves the computer on

PS: systemctl knows what it was started from by using argv[0], which is a standard construct in C, here is a snippet of systemctl source code (reduced tabs for readability):

int systemctl_dispatch_parse_argv(int argc, char *argv[]) {
    assert(argc >= 0);
    assert(argv);

    if (invoked_as(argv, "halt")) {
            arg_action = ACTION_HALT;
            return halt_parse_argv(argc, argv);

    } else if (invoked_as(argv, "poweroff")) {
            arg_action = ACTION_POWEROFF;
            return halt_parse_argv(argc, argv);

    } else if (invoked_as(argv, "reboot")) {
            arg_action = ACTION_REBOOT;
            return halt_parse_argv(argc, argv);

    } else if (invoked_as(argv, "shutdown")) {
            arg_action = ACTION_POWEROFF;
            return shutdown_parse_argv(argc, argv);