Napster used little bandwidth because you were connected to a central server. You did not need to know directly about other clients, the central server took care of that for you.

Example:

Search For "file"

Napster:
Your client asks the server for any files related to the keyword "file". The server the results it finds.

Gnutella:
Your client asks all connected clients for any files related to the keyword "file" the clients in turn search their local files for anything relevant and return the results. They also send the query to all the clients they are connected to ... and so on until the TTL expires on the query ( usually about 4 to 7 levels deep ).



I am not sure about Kazaa so someone who knows should correct me if I am wrong but I think it works on a central server like basis but with more "central servers".