Persistence is the space on your USB key the will be used to store information, so that that information is still there after a reboot. This tag MEANS THE SAME as persistent.
Live with persistence: You have the portability of live media with a home-folder and possibly other temp storage
Live without: Portability but no saved anything
LiveUSB with persistence: Less life out of the USB(a bunch more reads), but very similar to 1
LiveUSB without persistence: Less life out of the USB(a bunch more reads), but very similar to 2
Full install: Obviously, a full install to the USB would translate to shorter life since it would drastically increase the number of reads and writes.