Small correction: this is correlation operator. Deep learning wise they (correlation and convolution) are equivalent but in probability it will lead to incorrect results.
(Cross-)correlation is convolution with a reversed kernel (second signal) (or vice-versa, of course). (For discrete signals, reversing the kernel is just a swapping the indexes around; which makes absolutely no difference for deep-learning). Convolution is more "natural" because it's abelian, whereas swapping signal and kernel in cross-correlation time-reverses the result.