Mac App To Make External HDD Bootable
As far as I can see the Apple supported "createinstallmedia" command does not work with macOS versions prior to Mavericks.

However it is possible to restore the MacOS installer disk image (inside the installer .app package) to a USB thumb drive.


Using Disk utility format the USB drive with Mac OS Journaled format
Right-Click on the .app package for the version of MacOS that you want to create a bootable installer from and select Show Package Contents from the pop-up menu that appears.
Copy the .dmg file therein to your desktop. I forget what it is called but is will be several GB in size and the only one there.
Select the recently formatted USB key on the left side of Disk utility and find the "Restore" command. It may be in the Edit menu (Mojave) or an icon on the Disk Utility title bar.
Select the .dmg image file you copied to the desktop to restore from and click the restore button.


That will image the USB key using the installer .dmg file as the source. It will take 10 minutes or so but when you are done you will have a bootable USB key to install that version of macOS from.