I have the full blown OS installed on a USB drive, persistent and live.
Just to clarify, a system running from a USB in
persistent mode, is a Live system
capable of retain changes you make to it across reboots; install new programs, perform updates, customizations and so on. Likewise, a system running from a USB in Live mode and
no persistence enabled, is a Live system
uncapable of saving your changes across reboots; you can try and install stuff, change themes, however, every change you made to the Live OS,
will be lost upon reboot. In short;
1. You can install the OS to an HDD/SDD: changes will be saved.
.2 You can run the OS from a USB in live mode with persistence: the system keeps running in Live mode but changes will be saved.
3. You can run the OS from a USB in live mode without persistence: the system keeps running in Live mode but changes won't be saved.
Also, some distros like openSUSE, creates a COW(copy-on-write)partition in the USB when in Live mode, which allows a certain level of persistence; customizations made to the system like theme changing will be saved, as well as downloads, documents, wifi passwords, and anything else in the
/home directory will be available across reboots, but changes made to the system like updates and programs installed won't.