>I think I understand the client and (web)server approach, the difference here is that the data must be on the client as well. I know what you're going to say - chuck the server side on the client. Maybe?

No it doesn't have to be all on the server - that's the idea behind using the Internet as a network. You can have online/offline applications or true distributed applications where some processing occurs client side potentially with private data for the client and some public data that's provided by the server.

The amount of integration and data split depends on your needs for the application.