Actually you've got it almost all right. WebSphere Process Server is built on top of WebSphere Enterprise Services Bus, which is built on top of WebSphere Application Server. And yes, you even have what each product does correct also.
The best place to look for scenarios that describe how these are used in in the IBM Redbooks. This
redbook describes a BPM scenario that shows you how to use WPS, how to deploy applications to it, etc. This
redbook will help you get started with Websphere ESB. Finally, this
redbook shows you how to implement and deploy services for WebSphere Application Server.
Good luck! There's a lot to learn, but these are good places to start.