The inconsistency of VaadinSession?

I created an UI A containing another UI B as an embedded BrowserFrame component. When I compared the VaadinSessions ( obtained by UI.getSession() ) of these two UI instance, I found they are not identical ( i.e. the attributes added to the VaadinSession of UI A can’t be retrieved from the session of UI B). However, when I compared the ids of these two warped sessions, it turned out to be the same. I thought all the VaadinSessions for the components showing in the same browser should be identical. Should the VaadinSession work in this way or it is my own misunderstanding?