If I initiate a click with jquery which does window.open(), it is blocked by pop up blocker, If I do the click manually the window is not blocked. How does the browser differ between the two?
The Firefox implementation of this is discussed at length on this bug, and this other bug has some further interesting background, including what lengths sites will go through in order to foist an unwanted popup window on unsuspecting users (in this case: calling window.open() from within an image load event). If you search around Bugzilla you'll find that the Mozilla people took a number of years to get this all working correctly, for example here's a bug from 2001.
The way it works currently is this: When Firefox receives a click event from the operating system, for a certain amount of time window.open() is enabled in JavaScript (look for dom.disable_open_click_delay in about:config). If you call the click() event from code without a user click occurring then the first step, the enabling of window.open() never occurs, though the call to window.open() will itself succeed to stop sites detecting that you have popup blocking enabled.
I'm not sure how other browsers implement this stuff but it would be surprising to me if it was much different.