What is the difference between Default installation to a USB stick and Live Persistance USB installation?
The default just copy iso to usb stick to let you launch the live system.
Persistence gives you opportunity to save your settings in live session on your usb stick.
I mean if I fully install the Distro to an USB instead of internal SSD. Why should I use built in live USB with persistance tool? What is the difference?
You dont need persistence if you install Sparky on a hard drive.
It is useful if you use Sparky in live mode only, to save changes made in live session.