Perhaps a couple examples would help:
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If you rotate a gyro at constant speed, it will output angular velocity (degrees per second or rotations per minute if you like). When you stop rotation, output drops to zero. The output is always proportional to speed of rotation. If you integrate the output (add successive values) you can track absolute angular position. No rotation = zero, fast rotation = high value.
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If you rotate an accelerometer at constant speed, it wil output zero. When you stop rotation, output increases proportional to how fast you stop. The output is always proportional to change of speed. Constant speed = zero, quick stop (or start) = high value.
If you like math, you may find the following interesting:
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A plot of the integral of an accelerometer has the characteristic of a gyro.
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A plot of the derivative of a gyro has the characteristic of an accelerometer.