Of course there will be a difference. If you close your browser, you can open it again and see the same page. If you close the HTTP server (no matter which one), you won't be able to see any pages except those stored in the browser cache and not attempted to reload. :-)
I'm pretty much sure you wanted to know something else, but my reply should remind you to ask questions correctly.
[EDIT]
OK, as to the question: one of the names of the cookie is the
browser cookie. They are stored on the client side and belong to a particular browser and not related to a server:
http://en.wikipedia.org/wiki/HTTP_cookie[
^].
If should clear your concern.
—SA