How is that possible if you're comparing the same data loaded on the client vs the server? Server has a faster Internet connection and connects to the DB directly (not over HTTP).

Sure, clients load "faster" if you mean they don't actually load everything. Apples to oranges.

If a page needs to make 5 DB queries to present a bunch of data, those 5 DB queries will be faster on the server than from the browser. So will parsing the response and transforming it into HTML.