Transforming Tetrominoes

A tetromino is a shape made by putting four equal-sized squares together so that each square shares at least one side with another square. Neither flipping over nor turning changes the shape of a tetromino. Tetrominoes come in five shapes, called I, L, O, T and Z after the capital letters they most closely resemble. Which two tetrominoes cannot be converted into one another by re-positioning just one of the four squares?

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