"e.target" calling wrong target?

Behavior is as expected. Per MDN, event.target is

A reference to the object that dispatched the event. It is different from event.currentTarget when the event handler is called during the bubbling or capturing phase of the event.

The innermost element that was clicked on was the img, so the img is the target of the event.

If you wanted a reference to the element the handler is on, use e.currentTarget instead:

$('.star-span').click(e => {
  console.log(e.currentTarget);
});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>

<span class="star-span" id="1">
  	<img class="star-img" width="15%" src="https://upload.wikimedia.org/wikipedia/commons/thumb/1/18/Five-pointed_star.svg/2000px-Five-pointed_star.svg.png" />
</span>

What you are looking for is the e.currentTarget and not e.target. Check the snippet. e.currentTarget is what you assigned the listener to. e.target is what actually dispatches the event (whatever is under the mouse)

$(() => {
  	$('.star-span').click(e => {
  	  	console.log(e.currentTarget);
  	});
});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>

<span class="star-span" id="1">
  	<img class="star-img" width="15%" src="https://upload.wikimedia.org/wikipedia/commons/thumb/1/18/Five-pointed_star.svg/2000px-Five-pointed_star.svg.png" />
</span>

As others have answered using e.currentTarget can work. There is also one more way using function instead of arrow and you will have benefit of having this object also. You can also use e.currentTarget here.

$(() => {
    $('.star-span').click(function(e){
        console.log(this);
        console.log(e.currentTarget);
    });
});
<script src="https://ajax.googleapis.com/ajax/libs/jquery/2.1.1/jquery.min.js"></script>

<span class="star-span" id="1">
  	<img class="star-img" width="15%" src="https://upload.wikimedia.org/wikipedia/commons/thumb/1/18/Five-pointed_star.svg/2000px-Five-pointed_star.svg.png" />
</span>