You are correct that there are two different approaches in play here.
The 622 has the homeplug chip built in, so it just uses its power cord to connect to the power line network. The adapter picture that you posted, would be what you would use to connect your router to the power line network. So the adapter would plug in to the power outlet and an ethernet cable would connect the adapter to the router. That adapter would bridge between the ethernet and power line networks. That in turn would allow the 622 to communicate through its power cord, to the adapter, and then to the router.