I think @randomprincess's description comes closest,except according to the guide.
I have a Kindle, so I am not sure of exact page location 10634 of 23963). it is in Part Six, WDW w/ Kids.
On most FP attractions, Disney handles switching off somewhat differently. When you tell a cast member that you want to switch off, he or she will issue you a special "rider exchange" FP for 3 people. One parent and the nonriding child (or children) will at that point be asked to leave the line. When those riding reunite with waiting adult the waiting adult and two other persons fro the party can ride using the special FP.
and then a little further down:
B/c the rider exchange pass can be used by the adult holding it as well as by three companions, this yields a "four for the price of one" scenario in terms of FP currency.
It then goes on to describe how you could obtain many FPs at the same time with a group of a large enough size.
So no waiting in the regular line (this is a FP thing), but also different from the regular FP that you get out of the machine, b/c every riding person does not need to obtain a FP for any given ride.