Q:

what is the difference between these two systems?

what is the difference between these two pulley systems when calculating the angular acceleration if the moment of inertia and radius is the same?

A:

In left diagram the force F is creating a torque and only the pulley is being accelerated.
In the right hand diagram both the mass and the pulley are being accelerated by the weight of the mass.
The tension in the string is less that the weight of the mass as the mass is accelerating downwards.
So the angular acceleration of the pulley will be less in this case.

