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A Schmitt Trigger is a comparator, because it compares its input voltage to a "threshold" voltage, but it has _two_ threshold voltages (the upper and lower trigger voltages), and which threshold voltage is used depends on the output state.
If the input voltage is higher than the upper trigger voltage, the output will be high (for a non-inverting Schmitt trigger). In this state, the input is compared to the lower threshold voltage, so the input now has to go below the lower threshold voltage before the output will go low.
The threshold voltage depends on the output state, such that a high output selects the lower threshold voltage, and a low output selects the upper threshold voltage.
This can be visualised as using a fixed threshold but adding a small voltage (the difference between the upper and lower threshold voltages, also called the hysteresis voltage) to the input voltage before it is compared. This small added voltage is high when the output is high, and low when the output is low. A small amount of the output voltage is effectively being added to the input voltage before it is compared to a fixed threshold. This is positive feedback, also called regenerative feedback.
So a Schmitt trigger operates as a voltage comparator, and a small amount of the output is added to the input, so it uses positive or regenerative feedback.
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