what is the difference between free-fall acceleration and acceleration due to gravity?
None.
The very phrase "acceleration of free fall" seems clumsy and ambiguous to me. It implies that the strange entity free fall is the thing doing the accelration. Something like "acceleration in free fall" makes more sense. It is difficult, without knowing the original question, whether the disitinction between the two is valid or not. It seems to me that I have typically (perhaps only) heard free fall referred to falling within the atmosphere. In that case the acceleration is going to be strongly modified and eventually limited by air resistance. In this interpretation acceleration due to gravity and acceleration during free fall would be different.
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