A live USB is used for testing the distribution. It is also used for installing Linux on computer hard disk. Normally, any changes you made to your live distribution is lost and this limits the usage of the live USB.
This tutorial shows the steps for actually installing Ubuntu Linux on an external US drive with the bootloader installed on the USB. It is NOT live USB set up. This USB will work as portable operating system and can be used on any computer system. Any changes or installs on it, are retained.
See How to Actually Install Ubuntu on USB
This tutorial shows the steps for actually installing Ubuntu Linux on an external US drive with the bootloader installed on the USB.