i start tomcat by running startup.bat and there will be a small cmd-window running the tomcat. After that i wanted to stop tomcat and I close that window.
And topcat stopped. so what is the point of shutdown.bat?
Most applications can be shutdown in more than one way; there's the "graceful" way, where a program can clean up after itself; the less-than graceful way, where a program can try to catch a shutdown (termination) signal; and the harsh way, where a program is "killed" (kill -9 in unix). Closing the window is probably closer to the second way.
And of course it wouldn't work very well if you didn't have access to a windowing environment on a remote server.