Neither. While the BeOS and the Mac OS can be installed on the same system, only one operating system can actually be running at a time. In this regard, the BeOS is quite similar to MkLinux.
The normal process for booting the BeOS on a Power Mac involves booting the Mac OS. During the boot process, the Mac OS loads Be's "OS Chooser" extension. Loading the OS Chooser extension allows you to select an operating system to load. If you choose the BeOS, the Mac OS load process will stop, and the BeOS will take over the machine and begin to load.
If you instead load the Mac OS, you can later launch the BeOS by running the BeOS Launcher application. The BeOS Launcher will squeeze the Mac OS out of the way, and the BeOS will start up.
So that your machine does not wait during the boot process for you to make a selection, the OS Chooser extension remembers your most recent OS boot choice, and will choose that OS by default after a countdown of 5 seconds.