Are the effects of gravity and acceleration identical to the point that no sensor can tell the difference?
Imagine an accelerometer that is in a box, and held aloft by a rope which is attached to a pulley, balanced by another box of equal mass.
You could either:
1) Cut the rope. The box will fall downwards, being accelerated by gravity.
2) Push the box downwards with an acceleration of $9.81m/s^2$, from an ‘applied force’
The accelerometer can not distinguish between these two scenarios.