Usually with piggyback the person being "carried" who is holding on to the one doing the "carrying", and not necessarily the other way around. I would see carrying as situations where the one doing the carrying is holding onto the person that is being carried (whether the other way around applies or not).
Then again there are already a few images with the carrying tag thanks to the implication from shoulder carry that do not fit this eg. post #473334. This implication was made with no discussion, though, and in a topic (topic #4622) that didn't even mention that it contained this implication.
There is also currently no distinction like this in any of the wikis.