They'll both be connected to your router and the Ethernet cable will be taking priority, as it's a much more stable method of connection (I only wish I could have mine wired). The Wi-Fi will be showing as connected as it's a live available recognized network, but you don't need it to be connected at the same time. Whilst it could be acting as a redundancy connection in case something goes wrong with your wired connection. If you were just using your wired connection and it went wrong, most likely a cable fault and not an internet connection fault (as that would be an error is all cases), then there is nothing to stop you just simply turning on your Wi-Fi.
Personally, I'd turn it off as it's not really needed, even though the resource use would be negligible, there's no harm; besides, it's not like it's going to double your connection speed.