Ha, thin client ain't a pci slot card. It's more of an architecture involving a lot of thin clients and a "thick" server. The clients don't have a proper processor or a memory or storage and hence called a thin client.
There's no clear definition for thin clients. So the most that can be said of a thin client is that, it is a client that does as little processing as possible while relying on a powerful (or thick) server to do the rest of the processing. A thick client does as much work possible locally, relying less on the server.
The reason it is economical and faster is that, in a thick client environment, the processing power of a client is not completely utilized 99% of the time. If only we could provide this unutilized power to those machines that require it at that time... This is where the thick servers come in. They have all the processing power, does the requested processing and sends the result back to the client.
Find out more here:
*en.wikipedia.org/wiki/Thin_client