Storyswap

Storyswap swaps the characters based on their position and not their character. Asriel being the Papyrus of that universe would swap with chara who acts as the sans of that universe, and so on.

History Recast

History Recast swaps the characters based on themselves and not the positions. An example is that Frisk becomes the sans of that universe because they swap roles with chara in underswap so History Recast swaps them with them as well.

I hope that clears up the difference's between the AU's for people who didn't understand/know before. Thanks for reading!