Scott, I have watched two videos which describe the system in different ways. So if I'm confused, so are a lot of other people - some of them Toyota service people.
Whichever. The facts are that Toyota does it in a very high-tech way. Their hybrid cars are powered by both a gas engine and an electric motor in varying ways depending on the driving situation, and the battery in them is claimed to never need replacement. And their regular hybrids never need to be plugged in.
(They do have plug-in hybrids, also, but I know even less about those.)
My sister has been on the Prius train for years. I know she's gone through a couple, but don't know the reasons why she's moved from one vehicle to another. I know she's driving a 2nd generation right now, that she purchased used, and probably has a buttload of miles on it. If it was a matter of just putting in a rebuilt battery, she'd have gone that route, so I'm assuming her 1st gen just had too many issues besides a battery, and hence her move to a 2nd generation, and then on to the one she's driving now.
Here's a pretty decent schematic of the system. It does show the 4 different modes - electric only, electric/gas, battery recharge, and regenerative braking. Note that all power to and from the driving wheels goes through the transaxle that's coupled to the engine.
hyrid drive power flowsedit: well, that image won't load, you'll have to click on the link. Here's one that shows the system putting all power (EM and IC) through the transaxle, but without the 4 modes.