I've been reading up on DNN pruning techniques and came across filter pruning and channel pruning in CNNs. However, as was my understanding, confirmed by this paper:
Pruning a filter in layer $i$ is equivalent to pruning the corresponding channel in layer $i + 1$, which is generated by this specific filter.
That said, what is the difference between the two methods? If I want to prune an entire filter in some layer, why not prune the corresponding channel (with channel pruning) on the next layer?