I have seen people using pooling and subsampling synonymously. I have also seen people use them as different processes. I am not sure though if I have correctly inferred what they mean, when they use the terms with distinct meanings. I think these people mean that the pooling part is selecting a submatrix from an input matrix and the subsampling part is selecting yet another submatrix that satisfies some condition from the first submatrix.
So say we have a $100 \times 100$ image. We do $10 \times 10$ non-overlapping pooling with $5 \times 5$ max subsampling. That would mean we slide the $10 \times 10$ "pool" across the image in strides of 10 and at every step we select the $5 \times 5$ submatrix inside the pool that has the maximum sum. That $5 \times 5$ matrix is what comes out of the $10 \times 10$ pool at the current potion. So in the end we have a $50 \times 50$ image.
Can you confirm that this usage of the terms pooling and subsampling exists?
I inferred this definition, as I cannot make sense of how some people use the two terms otherwise. For example in this video, or rather the people from the paper he is talking about (which I can't find because he only has the author name on his slide and no year).