forward will forward the request to the new servlet/jsp. Any out.println() statements in the servlet from where you call the forward method would not be of any use. You can't even call response.getWriter() method in this case. You can only do that in the servlet to which the control has been forwaded.
include will process the included servlet/jsp and any out.println()/html stuff will be included, and then control will come back to the servlet/jsp that called include method.