Why is convolution filter used instead of correlation filter in CNN? When I saw the two results of applying convolution filter and correlation filter, the results have the same distribution and are just flipped. Why is convolution filter used instead of correlation filter in CNN?
Convolution (as a term) matches with what we are trying to do in a CNN: we are building a (sort of) filter to extract certain feature from a signal. What is the output of the filter when a given image (vector) is given as input? Best thought of as convolution between the input and the filter.

Correlation (as a term) would be preferred when we are dealing with two signals/inputs. Probably bit misleading applied to CNN feature extraction operation.

I think this is more to do with terminology. The magnitude will be same as you suggest. Flipping happens because convolution is generally calculated after flipping the filter vector representation.