They each use a different backend, and their web UI's are designed with their own unique backend in mind.

There is Photon, a third-party web UI/client that may someday be compatible with both Lemmy and Piefed, but currently only properly supports lemmy.

As far as I know, Piefed, Lemmy, and Mbin essentially are just displaying the data made available from ActivityPub in different ways, like the comment aggregation for crossposts.