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The thing is that to realise the potential energy, yu have to move something - therefore potential energy is movement that has been stored.
Think about how the item gained the potential energy - it gained it by being moved to a high shelf, or the top of the ladder. Either way there was movement to get the energy into the system.
Thermal energy is atomic vibration.
Chemical energy is associated with electron location and consequently the movement of electrons.
Electrical energy is electron flow.
Kinetic energy is moving masses.
If you allow for the special case of potential energy being stored movement leading to stored energy, then YES all energy is movement.
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Overhead, the Albatross hangs motionless upon the air,
And deep beneath the rolling waves,
In labyrinths of Coral Caves,
The Echo of a distant time
Comes willowing across the sand;
And everthing is Green and Submarine
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