The Java Plug-in for the Netscape browsers is a standard Netscape Plug-in (where the plug-in for Internet Explorer is an ActiveX control). When installed, it includes a full version of the Java 2 Standard Edition, version 1.3. This means it has the 1.3 version of the AWT and Swing classes, as well as all other Java classes that are part of the 1.3 release of the standard edition. This Java Runtime replaces the runtime that comes with the browser, so you get the latest and a standard version of the Java platform. On its own, the Plug-in doesn't communicate with any server, at least not in any special way beyond getting the applet from the web server.
In order to tell the browser to use the plugin, you need to modify the <APPLET> tag to point to the Plug-in. You can either do this manually, or use the HTML Converter tool that Sun provides. It is then the browser that communicates with a server to get the plugin.