mass - Acceleration of two falling objects with identical form and air drag but different masses

I have a theoretical question that has been bugging me and my peers for weeks now - and we have yet to settle on a concrete answer.

Imagine two balloons, one is filled with air, one with concrete. They are both the same size (and hence have the same air resistance). On the moon, we are taught at school that they would drop at the same rate, however on earth, they obviously don't - with the concrete falling faster.

Our reasoning was as follows: Air resistance is not a factor in this example, therefore the only other variable is the mass (density) of the two balloons.

If you were to change the medium from earth's atmospheric air to water, the air ballon floats as it is less dense than water (and therefore displaces more water than its mass), and consequently has an upwards buoyancy force acting on it. The concrete sinks for the same reasons.

Therefore in the medium of air, there is also, albeit somewhat reduced, bouyancy effect acting on the balloons - explaining why the concrete balloon falls faster.

Could someone please tell me if my logic is correct, and if not explaing to us what other forces are playing their part.

Thank you so much for clearing this up!