I have a web application (WAR file). When I deploy it through Eclipse 3.5 using the WTP tools, I am able to start the Tomcat server from within Eclipse and view all the page
It's just all definied in the context.xml which Eclipse has given to Tomcat. If you want to configure this behaviour, then doubleclick the Tomcat instance in the servers view and check the Server locations section. To achieve what you initially want/expected, you need to select Use Tomcat installation and if necessary also specify the Deploy path.