No, it stores an entirely new set of references to objects, as well as some of those objects themselves (any that are not identical to previously stored objects).

You cannot look at a commit on its own and know exactly how it's different from the previous commit, but you do have the complete new state. You have to look at the parent commit's references and do an object-by-object comparison to identify exact changes. On the other hand, when you look at a diff, you can see exactly what has changed, but you cannot produce the version that came before without also having a complete copy of the current version.