# Difference between CNN filter and channel pruning

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?