Live, Persistent or Full install to USB
A Live install to USB does not record any data to either the USB or internal disk. All new information for the session is temporarily recorded in RAM and deleted when the computer is shut down.
A Persistent Live install to USB includes a overlay layer in the form of Persistent file(s) or partition(s) (named writable, casper-rw or home-rw). These files or partitions store any changes to the filesystem or home directory between sessions. Persistent files or partitions can be located on the USB or on the internal drive.
A Full install to USB stores information to the USB the same as a Full install to the internal disk stores info to that disk.
Etcher, dd, Disks, and Startup Disk Creator create Live only systems. Unetbootin, YUMI, Universal and Ventoy use a file to store persistence. Rufus and mkusb will create persistent partitions.
A Live USB will use any swap file that it can find on the computer. this will temporarily store the data from RAM. Hibernation can be installed to a Persistent USB but not to a Live USB.