I think this is the basic question for J2EE web applications.

My boss told me web application is NOT client-server application. I argued
with him because browser is the client, and the server code put in server.
Then web application should be a client-server application. My understanding
is that a web application is an application that runs on a browser. But
client-server application is not necessary a web application.

Please advise. Thanks!!

Hummmm!! in terms of end client, browser is a client! But if you look at a bigger picture, all objects interacting with each other are clients to each other! Am I smoking something or what?

A couple of differences:
1) Yes, a web browser is a client, but it's a generic client, i.e. usually no customization is required on the web browser end. And most workstation has a web browser already installed, meanin
2) All the application elements (jsp, form beans, etc.) comes from the server itself, where deployment on the client-side is not required. Application updates on server only, no headache of managing client deployment issues (version control, synchronization, etc.)

On your view point (which is not wrong), a web browser can be consider as a client and a web/application server can be consider as a server. But in the industry, owing to the above features, we usually treat it differently and called it web applications. We usually refer "client-server" application to those with deployment using customized clients (where the client coupled with the application, probably embedded some of the logics of the application too).