The short answer is that both Linear and Circular Polarizers do the same thing. The actual polarization effects such as reducing reflections on glass surfaces, increasing color saturation in foliage, darkening a blue sky are the same with both Linear and Circular polarizers.
Circular Polarizers contains a Linear Polarizer component that does the main work of polarization, as well as a second layer inside the filter called a Quarter Wave Plate, which 'spins' the light after it goes through the linear layer and before it enters the camera lens.
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