I think the most mind-blowing aspect about it is that (PinSketch) sketches are identical in size to the bandwidth that would be required to just send the differ

I think the most mind-blowing aspect about it is that (PinSketch) sketches are identical in size to the bandwidth that would be required to just send the difference if you did know it ahead of time. Perhaps this intuition helps: imagine we have sets of positive numbers, and we know that the difference is at most 1 element. So there is one element that you have but I don't, or the other way around. In this case there is a very easy solution: just send the sum of all your elements. If it's larger than the sum of the receiver's element, the (absolute value of the) difference is exactly the element that one party has and the other doesn't. In a way, PinSketch is generalizing this "send sum of your elements" in such a way that it works for more than one difference.