page - You can use the Bean within the
JSP page with the
<jsp:useBean> element or any of the page's static include files, until the
page sends a response back to the client or forwards a request to another
file.
request - You can use the Bean from any JSP page processing the same
request, until a JSP page sends a response to the client or forwards the
request to another file. You can use the request object to access the Bean,
for example, request.getAttribute(beanInstanceName).
Basically, page and request scope both end when your JSP page finished
processing. So even if a FORM is sent to the client by JSP, when that FORM
is submitted it will be a new Request. I think the only difference between
page and request is if the bean persists between forward() calls.