The Earth attracts all bodies towards its centre with the same gravitational acceleration...this means that if two bodies of different masses are...

Yes, it is true that two different objects, dropped from
the same height, could not rach the ground at the same time, though the same
gravitational force is acting on them.

The element that
makes the difference in this case is not the mass of the objects, because the mass does
not exist in case of free falling, but the air
resistance.

On the moon, where there is no air resistance,
the objects will hit it's surface, at the same
time.

Therefore, two objects of different
masses and materials, dropped from the same height, will hit the surface of the Earth at
different moments.