Actually when a user clicks on an element, the event carries mouse position like pageX/pageY and clientX/clientY but using trigger to fire the event programmatically, there will be no real mouse positions because the click event fired without the mouse interaction, this is one big difference, at least I can think of. That's why the e/event object is different in both cases and it makes sense, IMO.
Update :
In other words, it's not a real click event but a simulation of that event and in this case it's a tailored peace, for example, this is the prototype of the initMouseEvent (with example and on MDN), which used with createEvent
object.initMouseEvent (eventName, bubbles, cancelable, view, detail, screenX, screenY, clientX, clientY, ctrlKey, altKey, shiftKey, metaKey, button, relatedTarget);
This used to simulate a mouse event in vanilla JavaScript (it may varies in different browsers), also look at this, so in case of jQuery it's (event object created by trigger) a tailored object that jQuery build for cross browser support when using trigger and it's not same as the one that is in real click event, completely two different objects.