It depends on the caching policy for the page and the method used for fetching the page in the first place. If you fetched the page via a POST, a refresh will re-send the POST data while putting the URL in a new window will issue a GET to the server.
If the original request is a GET, the behaviour depends on how the current page is cached. Hitting refresh will cause the browser to check back with the server for the page (but not necessarily any scripts or images). If the page is set to be cacheable then pasting the URL in a new window might well just pull the page out of cache without hitting the server.
Note that checking with the server won't necessarily cause the page to be regenerated or redownloaded as the browser can issue a conditional GET or a HEAD request to check whether the page has actually changed since last fetched. Also, while some of the actions might pull the page from the cache, there's no guarantee it will (and dynamically generated pages usually have to be set up properly to be considered cacheable at all).
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