Slowly Swapping is more of an identity swap rather than a body swap story.
The idea is that someone switches lives with someone but instead of it happening instantly it happens slowly sometimes one swap at a time. A lot of stories like these the swaps usually happen instantly but in this one the person has to cope with the swaps one by one.
What's also different about this story is that only one person (the person swapping) is aware of the swaps.
The only body part swap that has happened in this story (except for hair) is Karyn's breasts with Jon's but that's because Jon has swapped lives with Karyn which means that he was the one who made the wish about the breasts.
Hope that helps
