The Earth attracts all bodies towards its centre with the same gravitational acceleration...
this means that if two bodies of different masses are dropped from the same height they should reach the ground at the same time, but often it does not happen. What is the reason for that?
Two objects when dropped from the same height are not attracted towards the Earth by the same gravitational force. But the acceleration due to the force acting on them is the same as the force is proportional to their mass.
In spite of the acceleration due to the force of gravitation being the same it is seldom found that objects reach the ground at the same time when dropped from the same height as there are additional forces acting on the objects that are not dependent only on their mass.
The primary resistive force is that due to the air. When an object travels through air there is a resistive force acting in a direction opposite to that in which the object is moving. The force can vary due to the shape of the object, the mass of the object, etc.
The net acceleration on objects due to the force of gravity and the resistance due to air is not the same. This is the reason why two objects dropped from the same height usually do not strike the ground at the same time.
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.