Always think of fat clients as clients that can do processing of their own, i.e. they have a CPU. Examples include your home computer (it can process and display it's own data with software installed on the machine, it doesn't need anything else to display information). On the other hand, thin clients CANNOT process their own information: they are mere mediums of collecting/organising/displaying/printing data, thus allowing the user to access information/software that is stored elsewhere, like a projector. A more formal example of a thin client would be those computers you see in the library with no CPUs, they are just there so you can view information processed by a server that is located elsewhere. The computers themselves are just input/output media.
When classifying stuff as fat/thin client, always ask: can this system carry out the "processing" information process, or does it need to outsource that process?