which battery will supply the load?
Your alternator has a non-zero impedance, which is higher than the impedance of the partly-charged battery in this case. That's what causes the voltage to drop when the battery is connected.

Or, in other words: The alternator cannot deliver as much current as would be required to put the battery's terminals to 14V, so it delivers as much as it can and the voltage drops. - With higher rpm the picture (voltage) will likely change. Besides, note that an alternator -as the name suggests- produces (rectified) alternating current (AC) where peak voltage and RMS may differ, so be sure what you are measuring. (This is, by the way, one of the reasons why you should never run your car's engine without connected battery; the battery, like a giant capacitor, smoothes the system's voltage ripple and spikes away which would otherwise put significant stress on other electric components.)