> But then you have to store the entire before & after locally?

Yes, there is difference between two (as you say) and there is integrity (modification detection). In the case of comparing new assets in a pipeline to those that were created earlier, it sounds plausible both copies would be present.

> That's the entire point of using a hash for change detection.

This is called integrity protection. Change detection is the incorrect term to use here. Please see what I referenced earlier for first and second preimage.